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DIELECTR IC PHENOMENA OF OXIDES WITH FLUO RITE RELATED SUPER STRUCTURES By CHRISTOPHER GEORGE TURNER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FO R THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014
2014 Christopher Turner
To my parents, friends and everyone who h elped me push through the last four years
4 ACKNOWLEDGMENTS First, I w ould like to thank my advisor Dr. Juan C. Nino for his support and guidance. He gave me the opportunity to conduct research that always challenged me and through his knowledge and support allowed me to thoroughly enjoy my time in and out of the lab. I woul d also like to thank my parents for helping me get to where I am today. It has always been comforting to know that no matter how bad or great of a day I had they would always be there to love and support me. My brothers have also been a fantastic support t hroughout my graduate study by giving me a distraction from work every once in a while. Kathleen Moffitt has also been one of my biggest supporters, especially in times of high stress she was always there to calm my nerves. Her love and support through the proposal defense thesis writings, and her ability to listen to my science filled day was just the thing I needed in my life and I only wish I had met you sooner. I would like to thank all my friends who came to visit every football season and gave me a r eason to take Saturdays off every Fall Your support was always appreciated and a special shout out to my roommates Mo and Trey for putting up with my strange hours and letting me burn things in the kitchen every once in a while. There have also been a num ber of students and professors who have helped me with my research that deserve special mention, and they are as follows: Dr. David Tanner and Evan Thatcher (IR), Dr. Beverly Hi nojosa (DFT), Dr. Brendan Kennedy (Neutron), and Dr. Matt Suchomel (APS). The f riends at turntable.fm for providing constant music for the day and encouraging me throughout, thanks Indie Mix.
5 I would not have been able to get this far without the considerable help of previous and current Nino research group members. When I first came in they answered any and all questions I had and then later I then became the source of answers for younger members. I would like to give a special thanks to the following people: Roberto Esquivel for letting me tag along the Bi 2 Ti 2 O 7 synthesis process (e ven in understanding anything to do with crystallography, the magic of theoretical experiments and the joys and wonders of being in charge of purchasing, Trey Davis wh ile also having to li ve with me also had the added benefit of dealing with me at work, Alex Arias for teaching me all the basics of dielectrics that I was able to build on, Don Moore, Paul Johns, Hyuksu Han, Brit t nee Mound, George Baure, Mehrad Mehr, Soumi tra Su lekar Bryce Edwards, and all of the other undergraduate members who helped me along. Apart from the science and work I will always carry the memories of the off time at UF. Whether it was Ninolympics, Lab Basketball, Lab Office Darts, Kind of a Big Deal Friday, Food Truck Friday, and just everyday laughs to break up the monotony of writing a paper (and thesis).
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 10 LIST OF ABBREVIATIONS ................................ ................................ ........................... 13 LIST OF SYMBOLS ................................ ................................ ................................ ...... 14 ABSTRACT ................................ ................................ ................................ ................... 16 CHAPTE R 1 INTRODUCTORY REMARKS ................................ ................................ ................ 18 1.1 Statement of Problem and Motivation ................................ ............................... 18 1.2 Scientific Approach ................................ ................................ ........................... 19 1.3 Organization of Dissertation ................................ ................................ .............. 21 1.4 Contributions to the Field ................................ ................................ .................. 23 2 BACKGROUND ................................ ................................ ................................ ...... 25 2.1 Fluorite Related Superstructures ................................ ................................ ...... 25 2.1.1 The p yrochlore structure ................................ ................................ .......... 25 2.1.2 The defect fluorite structure ................................ ................................ ..... 29 2.2 The Bond Valence Model ................................ ................................ .................. 30 2.3 Polarization Mechanisms ................................ ................................ .................. 31 2.3.1 Electronic polarization ................................ ................................ ............. 32 2.3.2 Ionic polarization ................................ ................................ ..................... 34 2.3.3 Dipolar polarization ................................ ................................ .................. 35 2.3.4 Space charge polarization ................................ ................................ ....... 38 2.3.5 T he dielectric spectrum ................................ ................................ ........... 38 2.4 Dielectric Relaxation in Pyrochlores ................................ ................................ .. 39 2.5 Vibrational Spectroscopy ................................ ................................ .................. 42 2.5.1 Normal mode determination ................................ ................................ .... 42 2.5.2 Raman scattering ................................ ................................ .................... 43 2.5.3 Infrared absorption ................................ ................................ .................. 43 3 EXPERIMENTAL PROCEDURES AND PROCESSING ................................ ......... 45 3.1 Bi 2 Ti 2 O 7 Synthesis ................................ ................................ ............................ 45 3.1.1 Powder synthesis ................................ ................................ .................... 45 3.1.2 Pellet formation ................................ ................................ ....................... 45
7 3.2 Solid State Synthesis ................................ ................................ ........................ 46 3.2.1 Powder synthesis ................................ ................................ .................... 46 3.2.2 Pellet formation ................................ ................................ ....................... 47 3.3 Characterization ................................ ................................ ................................ 48 3.3.1 Structural characterization ................................ ................................ ....... 48 3.3.2 Infrared and Raman characterization ................................ ...................... 49 3.3.3 Diele ctric characterization ................................ ................................ ....... 49 3.4 Computational Methods ................................ ................................ .................... 50 4 CRYSTALLOGRAPHY OF Bi 2 Ti 2 O 7 AND OTHER PYROCHLORES ..................... 52 4.1 Introduction ................................ ................................ ................................ ....... 52 4.2 Crystal Structure of (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) ................................ 53 4.3 Crystal Structure of Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 ................................ .............................. 55 4.4 Structural Study of Bi 2 Ti 2 O 7 ................................ ................................ .............. 56 4.4.1 Synchrotron X ray diffraction ................................ ................................ ... 57 4.4.2 Neutron diffraction ................................ ................................ ................... 60 4.4.3 DFT calculations ................................ ................................ ...................... 63 4.5 Conclu sion ................................ ................................ ................................ ........ 66 5 DIELECTRIC PROPERTIES OF Bi 2 Ti 2 O 7 AND OTHER PYROCHLORES ............ 67 5.1 Introduction ................................ ................................ ................................ ....... 67 5.2 Dielectric Analysis of Bi 2 Ti 2 O 7 ................................ ................................ ........... 69 5.2.1 Dielectric analysis as a function of temperature ................................ ...... 69 5.2.2 Dielectric analysis as a function of frequency ................................ .......... 74 5.3 Dielectric properties of the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 system ....... 79 5.3.1 Dielectric analysis of (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) ..................... 79 5.3.2 Dielectric analysis of Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 ................................ .................. 81 5.4 Conclusion ................................ ................................ ................................ ........ 82 6 RAMAN AND IR PROPERTIES OF Bi 2 Ti 2 O 7 ................................ .......................... 83 6.1 Introduction ................................ ................................ ................................ ....... 83 6.2 Raman Spectroscopy ................................ ................................ ........................ 86 6.3 Infrared Spectroscopy ................................ ................................ ....................... 94 6.3.1 Reflectance spectra ................................ ................................ ................. 94 6.2.2 Kramers Kronig analysis ................................ ................................ ......... 95 6.2.3 Oscillator model analysis ................................ ................................ ......... 97 6.4 Conclusion ................................ ................................ ................................ ...... 101 7 ORIGIN OF DIELECTRIC RELAXATION IN PYROCHLORES ............................ 102 7.1 Introduction ................................ ................................ ................................ ..... 102 7.2 Discussion ................................ ................................ ................................ ...... 103 7.3 Conclusion ................................ ................................ ................................ ...... 110 8 DIELECTRIC PROPERTIES OF TYPE II Bi 3 NbO 7 ................................ ............... 112
8 8.1 Introduction ................................ ................................ ................................ ..... 1 12 8.2 Dielectric Spectroscopy ................................ ................................ .................. 113 8.3 Defect Fluorite Structure Dielectric Property Rel ationship .............................. 116 8.4 Conclusion ................................ ................................ ................................ ...... 125 9 DIELECTRIC RESPONSE AND PHASE TRANSITION OF Gd 3 NbO 7 .................. 126 9.1 Introduction ................................ ................................ ................................ ..... 126 9.2 Results and Discussion ................................ ................................ ................... 127 9.3 Conclusion ................................ ................................ ................................ ...... 133 10 SUMMARY AND FUTURE WORK ................................ ................................ ....... 135 10.1 Summary ................................ ................................ ................................ ...... 135 10.2 Future Work ................................ ................................ ................................ .. 137 APPENDIX A EQUIVALENT CIRCUIT A NALYSIS OF Bi 2 Ti 2 O 7 ................................ ................. 139 A.1 Introduction ................................ ................................ ................................ .... 139 A.2 Equivalen t C ircuit A nalysis ................................ ................................ ............. 140 B Bi 2 Ti 2 O 7 TEMPERATURE EFFECTS ON STRUCTURE AND DIE LECTRIC PROPERTIES ................................ ................................ ................................ ....... 147 LIST OF REFERENCES ................................ ................................ ............................. 149 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 163
9 LIST OF TABLES Table page 2 1 Pyrochlore (A 2 B 2 O 6 29 ................................ ............ 26 2 2 Pyrochlores and the conditions present for possible relaxation .......................... 41 3 1 The calcination and sintering times and temperatures for the solid state synthesized oxides. ................................ ................................ ............................ 47 4 1 The 2 positions and the a pparent lattice parameter of (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 ..... 54 4 2 Lattice Parameters of (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 ................................ ................................ ............................ 55 4 3 Refined positions and parameters of Bi 2 Ti 2 O7 at 3 K ................................ ......... 57 6 1 Optical modes for Bi 2 Ti 2 O 7 ................................ ................................ ................. 84 6 2 Parameters for Bi 2 Ti 2 O 7 in the Lorentzian fitting of the Raman spectra. ............. 90 6 3 The observed Raman vibrational mode frequencies of bismuth and titanate pyrochlores ................................ ................................ ................................ ......... 93 6 4 Parameters for the phonon modes in the 20 K infrared spectrum of Bi 2 Ti 2 O 7 . 99 7 1 Pyrochlores and the conditions present for possible relaxation ........................ 104 7 2 New pyrochlores from this work and the conditions present for possible relaxation ................................ ................................ ................................ .......... 105 8 1 Lattice parameters of Ln 3 NbO 7 (Ln = Dy, Er, Yb, Y) and Bi 3 NbO 7 ................... 117 9 1 Crystal data and refinement parameters of the two proposed low temperature Gd 3 NbO 7 ................................ ................................ ................................ ........... 131
10 LIST OF FIGURES Figure page 1 1 Dielectric relaxation in Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 pyrochlore ................................ ...... 19 2 1 The fluorite structure of CaF 2 ................................ ................................ ............. 25 2 2 The pyrochlore structure visualization. ................................ ............................... 27 2 3 The A 2 2 O 6 octahedral networks ................................ ........... 28 2 4  view of pyrochlores. ................................ ................................ ................... 29 2 5 The four main polarization mechanisms. ................................ ............................ 33 2 6 Dipolar polarization energy schematic. ................................ ............................... 35 2 7 Frequency response of a dielectric material for dipolar polarization. .................. 37 2 8 Real and imaginary p arts of the permittivity as a function of frequency, showing the contribution from the four polarization mechanism. ........................ 39 2 9 Dielectric relaxation for BZN shown at 2MHz vs temperature. ........................... 40 4 1 XRD patterns of (Sm 0.2 5 Yb 0.75 ) 2 Ti 2 O 7 (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 ................................ ................................ ........................... 53 4 2 Nelson Riley function for the lattice parameter calculations of (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and ( Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 .................. 54 4 3 XRD patterns of Sm 2 (Sn 0.25 Ti 0.75 ) 2 O 7 Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 and Sm 2 (Sn 0.75 Ti 0.25 ) 2 O 7 ................................ ................................ ........................... 56 4 4 High resolution XRD at temperatures from 6 k to 250 K. ................................ .... 58 4 5 Rietveld fit of the room temperature x ray diffraction pattern. ............................. 59 4 6 The lattice parameter between 6 K and 150 K ................................ ................... 60 4 7 Rietveld fit of the room temperature neutron diffraction pattern. ......................... 61 4 8 Temperature dependence of the lattice parameters of Bi 2 Ti 2 O 7 ........................ 63 5 1 The real and imaginary part of the dielectric permittivity as a function of temperature from 10 kHz ................................ ................................ .................... 70 5 2 Imaginary and real part of the dielectric permittivity as a function of temperature from 80 Hz to 2 MHz. ................................ ................................ ..... 71
11 5 3 Arrhenius plot of Bi 2 Ti 2 O 7 dielectric relaxation using Equation 5 1. .................... 72 5 4 Imaginary and real part of the dielectric permittivity as a function of temperatur e ................................ ................................ ................................ ....... 74 5 5 Frequency plo ts at varying temperatures of , and ........................... 76 5 6 Normalized functions of , and at 290 K. ................................ .......... 77 5 7 Frequency dependent plot of the real part of the dielectric permittivity. .............. 78 5 8 Imaginary and real part of the dielectric permittivity as a function of temperature from 10kHz to 2 Mhz S m Co mpound s ................................ ........... 80 5 9 Imaginary and real part of the dielectric permittivity as a function of temperature of Sm 2 (Sn 0.5 Ti 0.5 )O 7 ................................ ................................ ....... 81 6 1 Room temperature Raman spectra of Bi 2 Ti 2 O 7 powder and sintered pellet. ....... 87 6 2 Raman spectra fitted to a sum of Lorentzian functions. ................................ ... 88 6 3 Raman spectra fitted to a sum of Gaussian functions. ................................ .... 89 6 4 The reflectance of Bi 2 Ti 2 O 7 at temperatures between 20 and 300 K ................... 94 6 5 The rea l 2 Ti 2 O 7 at temperatures between 20 and 300K ................................ ................................ ......................... 96 6 6 2 Ti 2 O 7 at tempe ratures between 20 and 300 K. ................................ ................................ ....................... 96 6 7 2 Ti 2 O 7 at temperatures between 20 and 300 K. ................................ ................................ ....................... 97 7 1 The electron localization function (ELF) for a portion of the ( 11) plane .......... 108 7 2 The relative energy landscape ................................ ................................ .......... 109 8 1 Real and imaginary part of the permittivity of single crystal type II Bi 3 NbO 7 .... 114 8 2 Normalized functions of the imaginary components of the impedance ( ), admittance ( ), modulus ( ), and permittivity ( ) ................................ ........ 115 8 3 Experimental and theoretical permittivity of type II Bi 3 NbO 7 and Ln 3 NbO 7 defect fluorites. ................................ ................................ ................................ 118 8 4 TCC of defect fluorite Ln 3 NbO 7 and type II Bi 3 NbO 7 from 218 K to 350 K. ....... 120 8 5 BVS of Ln 3 NbO 7 and type II Bi 3 NbO 7 defect fluorite s ................................ ....... 122
12 8 6 BSI of Ln 3 NbO 7 and type II Bi 3 NbO 7 defect fluorite s ................................ ........ 123 8 7 GII of Ln 3 NbO 7 and type II Bi 3 NbO 7 defect fluorite s ................................ ......... 124 9 1 Real and imaginary components of the permittivity of Gd 3 NbO 7 ...................... 127 9 2 Arrhenius plot of temperature o f Gd 3 NbO 7 ................................ ....................... 129 9 2 Heat capaci ty of Gd 3 NbO 7 ................................ ................................ ............... 130 9 3 Infrared Spectroscopy of Gd 3 NbO 7 at 50 K, 300 K, and 360 K. ....................... 130 9 4 Imaginary and real part of the permittivity of Gd 3 TaO 7 ................................ ..... 132 A 1 ................................ ................................ ........... 141 A 2 ................................ ................................ ............. 142 A 3 Equivalent circuit showing different R, C, and CPE combinations .................... 143 A 4 Fit of the 210K to circuit in Figure A 3A ................................ ............................ 144 A 5 Fit of the 210K to circuit in Figure A 3B ................................ ............................ 145 B 1 A comparison of the temperature anomalies found in the specific heat, neutron diffraction and dielectric permittivity. ................................ .................... 148
13 LIST OF ABBREVIATIONS a.c. Alternating current ANL Argonne National Laboratory APS Advanced Photon Source ANSTO Australian Nuclear Science and Tech nology Organization BSI Bond Strain Index BVS Bond Valence Sum d.c. Direct current GII Global instability Index IR Infrared MLCC Multilayer ceramic capacitors OPAL Open Pool Australian Reactor
14 LIST OF SYMBOLS r Permittivity Dipole moment Distance between charges Real permittivity E loc Local electric field E ext External electric field (or applied field) m e Mass of an electron Z Atomic Number P Polarization q Charge o Natural frequency of vibration (resonant frequency) Frequency o Permittivity of free space Damping constant (friction coefficient) Hz Hertz N ion Number of ion pairs per cubic meter ion The natural frequency of vibration of the ion pairs M r Reduced mass of the system m Energy Barrier between two equivalent sites s Distance between two equivalent sites N dip Number of dipoles per cubic meter k 1.3806488 10 23 m 2 kg s 2 K 1 ) T Temperature
15 P s Static value of polarization Relaxati on time R ij The length of the bond between atoms i and j S ij The bond valence between atoms i and j R o Standard bond distance b An empirically derived constant BVS i The bond valence sum for ion i
16 Abstract of Dissertation Presented to the Graduate Sc hool of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DIELECTRIC PHENOMENA OF OXIDES WITH FLUORITE RELATED SUPER STRUCTURES By Christopher George Turner May 2014 Chair: Juan C Nino Major: Materials Science and Engineering Fluorite related super structures have been extensively studied due to their attractive composition dependent dielectric properties. A combination of their high permitt ivity values low dielectric loss, and low sintering temperatures (1000C 150) makes them ideal candidates for embedded capacitors Several pyrochlores and all Bi pyrochlores displa y an interesting dielectric phenomenon, dielectric relaxation A comprehensive investigation of the dielectric p henomena of fluorite related superstructures and a study of pyrochlore relaxation is the topic of this dissertation. A structural study of Bi 2 Ti 2 O 7 was performed using neutron diffraction, synchrotron x ray diffraction (SXRD), and DFT. Both the neutron and SXRD revealed displacements of the Bi cation to the 96 g site and the displacement 2 Ti 2 O 7 are similar to that observed in another bismuth pyrochlore, Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 (BZN). 1 3 Nonetheless, what is striking is that displacement would occur without atomic substitutions and multiple site occupancy like in BZN and related pyrochlores.
17 Raman and IR studies also suggest displacements in the atomic positions of bismut h and oxygen away from their higher symmetry conventional pyrochlore Wyckoff positions and are show strong and surprising evidence of disorder at the titanium site. As for dielectric properties, Cubic pyrochlore Bi 2 Ti 2 O 7 was found to have a low frequency ( <10 kHz) and relatively high temperature (~125 K) dielectric relaxation was observed in Bi 2 Ti 2 O 7 An Arrhenius function was used to model the relaxation behavior and yielded an activation energy of 0.162 eV and an attempt jump frequency of ~1MHz. This res ponse is consistent with space charge polarization and not the result of dipolar or ionic disorder. T he work presented in this dissertation adds a final link to the question of what conditions are required in pyrochlores to exhibit dielectric relaxation An in depth investigation into the structure and dielectric properties of Bi 2 Ti 2 O 7 showed that a pyrochlore displaying atomic displacements without substitution does not display relaxation. This result points suggests that substitutional cations play a maj or role in the origin of dielectric relaxation in pyrochlores.
18 CHAPTER 1 INTRO DUCTORY REMARKS 1.1 Statement of Problem and Motivation The storage of energy in materials is of great interest due to the boom in the technology industry. As devices become sma ller and more integrated; efforts in the miniaturization of electronic components, such as capacitors, require new materials with improved dielectric properties. 4 5 Materials with superior dielectric properties (high permittivity and low loss) would allow for capacitors to significantly decrease in size. 6 7 T he fluorite structure ( AO 2 ) is considered to be one of the most flexible structures for its ability to form superstructures or derivatives. 8 The pyrochlore structure ( A 2 B 2 O 7 ) can be seen as an anion deficient fluorite related structure that is able to maintain the closed packed layers of cations throughout. Pyrochlores and other fluorite related structures can accommodate various cations on both the A site and B site. This cation flexibility allows compounds with fluorite related structures to exhibit interesting properties, such as: conductivity ( e.g Gd 2 Zr 2 O 7 9 11 ), dielectric properties ( e.g. Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 12 14 ) ferroelectric properties ( e.g. Cd 2 Nb 2 O 7 15 16 ), magnetic properties ( e.g. Gd 2 Ru 2 O 7 17 18 ), and photocatalytic activity ( e.g. La 3 NbO 7 19 ) Bismuth based pyrochlores have been extensively studied due to their attrac tive composition dependent dielectric properties. 12 20 24 A combination of their high permittivity values (usuall y above 100), low dielectric loss, and low sintering temperatures (1000C 150) makes them ideal candidates for embedded capacitors and multilayer ceramic capacitors (MLCC). Several pyrochlores and most Bi pyrochlores display an interesting dielectric ph enomenon, dielectric relaxation (Figure 1 1), where o n cooling below room temperature, these materials exhibit a step like
19 decrease in the real part of the dielectric permittivity accompanied by a broad frequency depende nt peak in the imaginary part. There are several proposed explanations for the observed relaxation in Bi pyrochlores, 12 23 25 however, there is no definite answer as to what induces this dielectric behavior in Bi pyrochlores. To address this issue an in depth investigation into cubic pyrochlores is needed in order to achieve a fundamental understanding of the necessary conditions to display dielectric relaxation in pyrochlores. Figure 1 1. Dielectric relaxation in Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 pyrochlore. In addition, other compounds with anion deficient fluorite related ( A 2 B 2 O 7 ) structures, such as weberites, were investigated to help elucidate the dielectric response of fluorite related superstructures. 1.2 Scientific Approach With the aim of identifying the conditions necessary for pyrochlores to exhibit dielectric relaxation, key pyrochlores were selected synthesized, and characterized. The achievement of synthesizing and sintering phase pure Bi 2 Ti 2 O 7 26 has opened the door for in depth studies into the dielectric properties, structure, and even provide insight into the dielectric relaxation phenomena in bismuth based pyrochlores.
20 In an effort to investigate the role of atomic displacements on pyrochlore dielectric relaxation, an in depth structural stu dy was performed using both neutron and high resolution x ray diffraction on Bi 2 Ti 2 O 7 Both the high resolution x ray diffraction, conducted at the Advanced Photon Source (APS) of Argonne National Laboratory (ANL), and neutron diffraction studies, conducte d at the Open Pool Australian Lightwater Reactor (OPAL) at the Australian Nuclear Science and Technology Organization (ANSTO), were performed down to cryogenic temperatures (~6 K) in order to compare any structural changes with the associated dielectric re sponse in Bi 2 Ti 2 O 7 The presence of atomic displacements in Sm pyrochlores was also probed through x ray diffraction. The second step of this research was to provide an in depth dielectric characterization of fully sintered phase pure Bi 2 Ti 2 O 7 and other Sm pyrochlores The dielectric properties of Bi 2 Ti 2 O 7 were comprehensively studied as a function of temperature and frequency in order to clarify the presence of relaxation in this material, and in turn, better understand the nature of the dielectric relaxat ion phenomena observed in Bi pyrochlores. Along with Bi 2 Ti 2 O 7 other key pyrochlores are also investigated in order to fully understand the conditions required for dielectric relaxation in pyrochlores. Vibrational spectroscopy can relate the phonon modes w ith the observed dielectric properties and, perhaps even more importantly for the case of Bi 2 Ti 2 O 7 gain an insight into the nature and characteristics of the local structure of Bi 2 Ti 2 O 7. This will be accomplished by analysis of Raman and IR (infrared) spe ctra collected at room and cryogenic temperatures.
21 The next research area aims to understand what conditions are necessary to be present in pyrochlores for dielectric relaxation. In order to accomplish this goal several newly synthesized pyrochlores, inclu ding Bi 2 Ti 2 O 7 and a comprehensive literature review of other Bi pyrochlores will be presented, experimentally determining what factors are necessary to be present in pyrochlores in order to exhibit dielectric relaxation. An investigation into the structur e property relationship of a fluorite related compound, Bi 3 NbO 7 will be presented and will link its dielectric response to its unique structure using Bond Valence Sum (BVS) analysis. Finally, of Gd 3 NbO 7 structure will be discussed by comparing the dielect ric response of Gd 3 NbO 7 with Gd 3 TaO 7 and linking their response with complimentary structure data (HR XRD, IR). These results not only contribute to the identification of structure dielectric property relationships in fluorite related super structures, bu t also provides a definitive answer for the necessary conditions for dielectric relaxation in pyrochlores. 1.3 Organization of Dissertation Chapter 2 provides background information necessary for a better understanding of the work presented in subsequent c hapters. Information regarding fluorite related superstructures, polarization mechanisms, vibrational spectroscopy, bond valence sum model, and impedance and dielectric spectroscopy is provided. Chapter 3 discusses the experimental procedures, including sa mple preparation and materials characterization techniques, used in the execution of the research. Chapter 4 reports the crystallographic study performed on Bi 2 Ti 2 O 7 (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 (where x = 0, 0.25, 0.5, 0.75, and 1 for all compo unds).
22 Both neutron and synchrotron x ray diffraction results are presented at varying temperatures (6 K 400 K) for Bi 2 Ti 2 O 7 Crystallographic refinements of Bi 2 Ti 2 O 7 are also presented at room and cr yogenic temperatures. The Sm pyrochlores are also exam ined in order to discern the presence of displacements from the ideal pyrochlore structure, one of the possible factors contributing to dielectric relaxation. Chapter 5 reports the dielectric properties for Bi 2 Ti 2 O 7 and the Sm pyroc hlores investiga ted in C hapter 4 An in depth study of the dielectric properties of Bi 2 Ti 2 O 7 were measured as a function of frequency (40 Hz 2MHz) and temperature (20 K 500 K). The d ielectric response of other key pyrochlores were investigated to probe for the presence of d ielectric relaxation. Chapter 6 includes the analysis of Raman and infrared (IR) spectroscopy studies in Bi 2 Ti 2 O 7 A detailed analysis linking non correlated atomic displacements to the Raman and IR spectra is presented. The nuclear site group analysis is used to ascribe the possible modes in both the IR and Raman spectra. Oscillator models are utilized to fit the spectrum and calculate the real and imaginary contributions of the permittivity. Chapter 7 presents a summary of the dielectric response of pyr ochlores previously studied along with that of the pyrochlores selected in this study to help elucidate the nature of dielectric relaxation. This C hapter presents what factors are required to be present in any pyrochlore in order to display the dielectric relaxation phenomena. Chapter 8 covers correlations between dielectric properties and crystal structure of Bi 3 NbO 7 A detailed dielectric analysis as a function of frequency and temperature shows the transition from an insulating behavior to conduction. A comparison between
23 the structure of Bi 3 NbO 7 and other Ln 3 NbO 7 defect fluorites is performed using Bond Valence Sum (BVS) analysis and then compared to their dielectric responses. Chapter 9 presents the structure of Gd 3 NbO 7 in a new light by comparing its d ielectric response to that of Gd 3 TaO 7 By using this dielectric comparison and other complimentary structural data, the low temperature phase of Gd 3 NbO 7 is presented. Chapter 10 presents a summary of the dissertation and discusses the future work in the re levant research areas. At the end of the thesis, there is an appendix section appendix A on fitting the relaxation behavior of Bi 2 Ti 2 O 7 to an equiv alent circuit. 1.4 Contributions to the Field The structure and atomic positions of Bi 2 Ti 2 O 7 was reported fo r the first time using n eutron diffraction and synchrotron x ray diffraction. Atomic displacements in the A An in depth study focusing on neutron HR XRD and DFT simulations is in preparation for public ation. 27 A thorough electrical characterization of Bi 2 Ti 2 O 7 was perform ed thor ough electrical charac terization (first time bulk values have been characterized) Bi 2 Ti 2 O 7 displays space charge relaxation near room temperatures at low frequency range. This work was also published in the Journal of the American Ceramics Society 28 Bi 2 Ti 2 O 7 does not display typical dipolar Bi pyrochlore relaxation behavior a nd most importantly, t hat chemical substitution is a necessary condition for dielectric relaxation in bismuth ba sed pyrochlores. A Raman and infrared characterization of Bi 2 Ti 2 O 7 was characterized for the first time in the field. Evidence of Bi cation displacement s was found by the overlap of infrared F 1u modes in the Raman spectra. Evidence of the displacement upon the Ti
24 cation as observed by analysis of phonon mode interactions. This work has been submitted to the Physical Review B journal. 29 By investiga ting the dielectric response of the Bi 2 Ti 2 O 7 (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 pyrochlore systems the impact of cation substitutions and atomic displacements on relaxation was targeted. The absence of dielectric relaxation in these systems prove that in order to display dielectric relaxation in pyrochlores it is necessary to have both atomic displacements and cation substitutions The dielectric properties of Type II Bi 3 NbO 7 single crystal were studied for the first time. The real part of permittivity increases with an increase in Ln 3+ ionic radius and an increased divergence from the Cla usius Mossotti E quation is observed when applied to the type II Bi 3 NbO 7 with large dipolar contributions. This work was submitted for publication in the Journal of Soli d State Chemistry. 30 The author has also synthesized and characterized dielectric tests on Gd 3 Ta O 7 and the structural transition of Gd 3 NbO 7 is Cm 2 m at low temperatures. 31 Along with the main works presented in this dissertation the author ha s been involved in the dielectric characterization of BaTiO 3 and BiNb 3 O 9 which have been published in the Journal of Applied Physics 32 and the Journal of Solid State Chemistry 33 respectively.
25 CHAPTER 2 BACKGROUND The present C hapter briefly summarizes some of the theoretical background required for understanding the work covered in this dissertation 2.1 Fluorite Related Superstructures The fluori te structure serves as the building blocks for fluorite superstructures such as pyrochlores, weberites and defect fluorites. These superstructures are best described in relation to the fluorite crystal structure. In the cubic fluorite structure ( M X 2 ), M 2+ cations are located at the face centered sites and the X 1 anions are located at the tetrahedral sites as shown in Figure 2 1 for CaF 2 Figure 2 1. The fluorite structure of CaF 2 2.1.1 The pyrochlore s tructure The oxide pyrochlore structure is p resented as A 2 B 2 O 6 to represent the four distinct crystallographic atomic sites, where the A cations are typically +3 and the B cations are of +4 charge. Pyrochlores are assigned the space group (space group 227) containing eight molecules per unit cell (Z = 8). Th e A cation (~ 1 ionic radius) and surrounding oxygen form an eight fold coordinated distorted cube (scalenohedra),
26 The B cations are typically smaller (~ 0.6 ionic r adius) and are six fold coordinated with O atoms, all at equal distances from the center B atom, to form trigonal antiprisms. The coordination states of the cations are often referred to as octahedral (A cation) and cubic (B cation). 34 If the A cation is lo cated at the origin of the pyrochlore it is said to be origin choice 1, for a B cation at the origin it is origin choice 2. Typically, and for the purposes of this thesis all pyrochlores will be discussed based on origin choice 2, unless otherwise specifie d. The location of the atoms, site symmetry and atomic coordinates are given in Table 2 1. Table 2 1. Pyrochlore (A 2 B 2 O 6 34 Atoms Wyckoff Position Site Symmetry Atomic Position x y z A 16 d (D 3d ) 0.5 0.5 0.5 B 16 c (D 3d ) 0 0 0 O 48 f mm (C 2v ) x 1/8 1/8 8 b (T d ) 3/8 3/8 3/8 Description of the Pyrochlore Structure There are many different ways to describe the pyrochlore structure. One method is to base the pyrochlore structure off of the fluorite str ucture. Incorporating A 3+ and B 4+ cations to face centered sites of the fluorite structure will lead to an anion deficient fluorite unit cell (Figure 2 2B). One pyrochlore unit cell edge length is twice that of a unit cell of CaF 2 therefore allowing eigh t unit cells of the anion deficient fluorite structure to fit inside the pyrochlore unit cell (Figure 2 2C).
27 C Figure 2 2. The pyrochlo re structure visualization. A) t he fluorite structure, B) an anion deficient fluorite, C) two of the eight a nion deficient structures arranged in the pyrochlore unit cell. The pyrochlore structure can also be described as two interpenetrating networks ( Figure 2 3 ) The BO 6 octahedra form a corner shared octahedral network, while A 2 tetrahedral substructures a re found in the empty channels formed by the BO 6 octahedra. B Vacant Site A O A B
28 Figure 2 3. The A 2 and B 2 O 6 octahedral networks that make up the pyrochlore structure For an ideal pyrochlore, using origin choice 2, six of the seven oxygen ions is located at Wyckoff position 48 f ( x 1/8, 1/8). The x parameter can vary from 0.3125, leading to perfect BO 6 octahedra and distorted AO 8 cubes, to an x of 0.375, leading to distorted BO 6 octahedra and regular AO 8 cubes ( Figure 2 4).
29 A B C Figure 2 4. [ 001] view of pyrochlores. A) When x = 0.3125 (perfect BO 6 octahedra) B) x is between 0.3125 and 0.375 (both BO 6 octahedra and AO 8 cubes are distorted) C) x = 0.375 (perfect AO 8 cubes) 2.1.2 The d efect fluorite s tructure The crystal structure of Ln 3 NbO 7 where Ln = a lanthanide series cation with a +3 charge, has been shown to shift from an orthorhombic weberite type structure to a cubic defect fluorite with decreasing Ln 3+ ionic radius. 35 37
30 Cubic defect fluorite structures occur in Ln 3 NbO 7 when the ionic radius of the Ln 3+ cation is less than or equal to that of Dy 3+ (1.027 ). 36 The defect fluorite structure has both disordered cations as well as disordered oxygen deficiency sites, unlike the pyrochlore in which the A B cations, and the oxygen vacancy sites have an ordered arrangement. 38 Visually it can be regarded as a disordered anion deficient fluorite similar to what is shown in Figure 2 2B. 2. 2 The Bond Valence Model The bond valence sum (BVS) model 39 41 is a common technique used for analyzing coordination and bonding in solid state chemistry. A bond valence is assigned to each bond in a structure based on the bond distance and types of ions involved in the bond. The bond valence (S ij ) for all atoms is calculated as: (2 1) where R ij is the length of the bond between atoms i and j R o is the standard bond distance between atoms i and j and b is an empirically derived constant, normally found close to 0.37. 39 The bond valence sum (BVS) for an ion is equal to the sum of all of the surro unding bond valences of the ion, with positive values for cations and negative values for anions: (2 2) A lower absolute value of BVS i indicate s that the ion is under coordinated, while higher values indicate an over coordination.
31 La ttice induced strains can be identified by a large value of the bond strain index (BSI) defined as: (2 3) where S is the experimental bond valence calculated from the observed bond length and s is the theoretical bond valence. The angle brackets indicate an average taken over all bonds in the formula unit. A structure is typically considered strained when the BSI is greater than 0.05 valence units (vu). 39 A second and complimentary measure of lattice strain is the global instability index (GII), the root mean square of the deviation of the BVSs from the ir expected values for all the at oms in the unit cell, shown in Eq uation 2 4: (2 4) where N is the number of atoms in the unit cell and BVS o is the expected bond valence sum. Values of GII less than 0.05 vu suggest that little or no strain is present while values greater than 0.2 vu indicate that the structure is very strained. 39 2.3 Polarization Mechanisms When a dielectric material is exposed to an electromagnetic field, the electric field will cause a displacement of negative and positive charges. This polarization of charge can happen thr ough the displacement of charge in individual atoms or molecules, the orientation of existing dipoles toward the direction of the field, or the separation of mobile charge carriers at the interfaces of impurities or other defect boundaries. 42 The polarization (P) can be determi ned by the dipole moments (): (2 5)
32 w between the charges One can relate the dielectric permittivity ( ) with polarization: (2 6) 0 is the per mittivity of free space, and E loc is the local electric field to which the atom is subjected to. Equation 2 6 basically shows that the more polarizable a medium the greater its dielectric permittivity. The polarizability ( ) of an atom or ion is defined as : (2 7) The microscopic polarization phenomena ( ) can be linked to the macroscopic term by using the Clausius Mossotti E quation: (2 8) There are four main types of polarization mechanisms ( when only considering linear dielectric materials): 1. Electronic polarization 2. Ionic polarization 3. Dipolar polarization 4. Space charge or interfacial polarization Each type of polari zation ( Figure 2 5 ) is present at different time domains; which is why the degr ee of the overall polarization depends on the time variation of the electric field. 2.3.1 Electronic polarization Electronic polarization occurs when the electron cloud is displaced relative to its nucleus and its surroundings. It is active at most freque ncies up to ~ 10 15 Hz, where it no longer responds to the electric field.
33 Polarization Mechanisms Unpolarized State Polarized State Space Charge Dipolar Ionic Atomic Figure 2 5 The four main polarization mechanisms. (Diagram from Mou lson and Herbert 43 )
34 Electronic polarization occurs in all materials and because it does not involve the hopping of ions or atoms it is temperature insensitive. The contribution of electronic polarization to the real and ima ginary components of the permittivity (assuming E loc = E ext ) are: (2 9) (2 10) where Z is the atomic number, m e o is the nat ural frequency o is the permittivity of free space and is a damping constant. 2.3.2 Ionic p olarization Under an electric field the positive and negative ions will displace according to the direction of the field. The contribution of ionic polarization is active up until the infrared frequency range (~ 10 12 10 13 Hz). The contribution to the real and imaginary components of the permittivity for ionic polarization are very similar to those s hown in Equations 2 11 and 2 12: (2 11) (2 12) w here N ion is the number of ion pai rs per cubic meter, ion is the natural frequency of vibration of the ion pair, M r is the reduced mass of the system. Similar to electronic
35 polarization, ionic polarization is temperature independent and stronger bonds with higher ion values are less read ily polarized. 2.3.3 Dipolar polarization Unlike electronic and ionic polarization, which occur at very high frequencies ( > 10 12 Hz), dipolar relaxation occurs at lower frequencies (10 4 < < 10 10 Hz) and plays an important role in determining the capaci tive properties of materials to be used in low frequency applications. Dipolar polarization arises from the reorientation and alignment of permanent dipoles due to an exte rnal field. In solids, ions preferentially occupy equivalent or near equivalent latt ice sites as a result of the applied field, s hown schematically in Figure 2 6 An ion is localized in an energy well in one of the two equivalent sites (Figure 2 6 A). H m s Without the presence of an electric field (Figure 2 6 A), each site has an equal probability of being occupied and there is no net polarization. When an elect ric field is applie d (Figure 2 6 B) the two sites are no longer equivalent, resulting in a bias towards one of the sites and creating a net polarization, this phenomenon is called ion jump polarization. 43 A B Figure 2 6 Dipolar polarizat ion energy schematic. A) energy versus distance d iagram under no applied field. B) under an applied field a bias occurs to one site relative to the other. (Diagram adapted from Moulson and Herbert 43 )
36 The dipolar mechanism c ontributions to the permittivity, under static conditions, are given by: (2 13) where N dip is the number of dipoles per cubic meter, s is the separation distance of t he two equivalent sites ( Figure 2 5), k is B T is temperature (K) It is important to note that E quation 2 9 applies to the dipolar contributions under static (d.c.) conditions, also increasing the temperature will reduce the permittivity contributed by dipolar polarization d ue to thermal randomization. In order to understand the behavior of dipolar polarization under dynamic (a.c.) conditions a mathematical model was created by Debye 44 to describe the properties of polar molecules and gases. Unlike ionic and electronic polarization, dipolar polarization does not occur instantaneously under the application of an electric field. A slower polarization mechanism occurs due to the dipolar reorientation ( P ) until it reaches its final static value ( P s ). The rate at time t at which P increases is proportional to the diff erence between the static value and the present value, where 1/ is the proportionality constant. This is expressed in E quation 2 14 : (2 14) where is the relaxation time of the dipole moment of the molecule. Another important as sumption to describe dipolar relaxation under the Debye model is that the relative dielectric constant is given by = + where represents the contributions to the permittivity at frequencies much higher than dipolar (i.e. electronic and ioni c
37 polarization). It is also required that as the frequency tends to zero = s the static dielectric constant. From these assumptions it can be shown that: ( 2 15 ) ( 2 16 ) These E quations are known as the Debye E quations and their variation with frequency for a material showing Debye relaxation is shown in Figure 2 7 Figure 2 7 Frequency response of a dielectric material for dipolar polarization. (Diagram adapted from Kao 42 ) The avera ge residence time ( ) (or relaxation time) of an atom or ion at any given site is also temperature dependent: (2 17)
38 where 1/ o is the att empt jump frequency and E a is the activation energy of relaxation, and k nstant. This shows that as the temperature increases, the atoms vibrate faster and are capable of following the applied field to higher frequencies. 43 2.3.4 Spa ce c harge p olarization Space charge, or interfacial polarizatio n, is produced by the separation of mobile positively and negatively charged particles under an applied field; space charge relaxation occurs at the lowest frequencies (up to 10 6 Hz). These charges can form in the bulk of the material or at the interface b etween two different materials. Like dipolar polarization, space charge polarization does not occur instantaneously under an electric field and undergoes a relaxation effect rather than a resonance. 2.3.5 The d ielectric s pectrum For most materials there ex ists more than one active polarization mechanism total electronic ionic dipolar space charge. As the frequency increases, various polarization mechanisms will be unable to keep up with the field and wi ll drop off ( Figure 2 8 ) Polarizations associated with vibrations of electrons (i.e. electronic polarization) or with vibrations of atoms (i.e. ionic polarization) belong to the resonance regime because a resonance will occur when the frequency of the app lied field is close to the natural frequency of the vibration or oscillation of the system. Polarizations involving the movements of dipoles (i.e. dipolar relaxation) or through the migration of charge carriers (i.e. space charge polarization) belong to th e relaxation regime as during their polarization/depolarization process, a relaxation phenomenon occurs. 42
39 Figure 2 8 Real and imaginary parts of the permittivity as a function of frequency, showing the contribution from the four polarization mechanism. Space charge and dip olar mechanisms are relaxation process while ionic and electronic are resonance processes. (Diagram adapted from Moulson and Herbert 43 ) 2.4 Dielectric Relaxation in Pyrochlores Bismuth based pyrochlores have been extensively studied due to their attractive composition dependent dielectric properties. 12 20 24 A combination of high permi ttivity
40 values (usually above 100), low dielectric loss, and low sintering temperatures make them good materials for dielectric components. However, all Bi pyrochlores and several non Bi pyrochlores display a dielectric phenomenon where : o n cooling below r oom temperature these materials exhibit a step like decrease in the real part of the dielectric permittivity accompanied by a broad frequency dependent peak in the imaginary part (Figure 2 8). As a consequence of this relaxation, at microwave frequencies t he temperature at which the dielectric peaks (T m ) displaces towards room temperature thus limiting GHz frequency applications. 1 45 Figure 2 9 Dielectric relaxation for BZN shown at 2MHz vs temperature. Arrhenius type E quations have been used to describe the dipolar glass systems that display similar relaxations and have been proven to successfully model the therm ally activated processes underlying the phenomena. 46 By employing the Arrhenius E quation, the Debye model corresponding to a single relaxation time can be followed to
41 fit the data and obtain meaningful physical values for the activation energy (E a ) and attempt jump frequency ( v o ) of the relaxation phenomenon: (2 18) where v r is the frequency of the relaxation peak in the imaginary part of the permittivity, and k B is the Boltzmann constant. All of the pyrochlores that exhibi t dielectric relaxation are presented in T able 2 2, a review of these pyrochlores showed three main characteristics that have been proposed to induce relaxation: 1. A polarizable lone pair cation occupies the A site 2. There is cation substitution 3. Atomic displa cement is present An in dept h discussion into which factors are necessary for dielectric relaxation to occur in pyrochlores is presented in Chapter 6. Table 2 2. Pyrochlores and the conditions present for possible relaxation Material Polarizable Lone Pa ir A site A and B site substitution A site substitution B site substitution Atomic Displacements Relaxation Bi 2 ( ScNb ) O 7 21 Yes -No Yes Yes Yes Bi 2 ( ScTa )O 7 21 Yes -No Yes Yes Yes (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 13 Yes Yes --Yes Yes (Bi 1.5 Zn 1.5 )(Zn 0.5 Ta 1.5 )O 7 25 Yes Yes --Yes Yes Bi 1.657 Fe 1.092 Nb 1.150 O 7 24 Yes Yes --Yes Yes Bi 1.67 Mg 0.64 Nb 1.53 O 7 47 Yes Yes --Yes Yes Bi 1.68 Ni 0.747 Nb 1.493 O 7 47 Yes Yes --Yes Yes Bi 1.657 (Fe 0.983 Al 0.109 )Nb 1.150 O 7 48 Yes Yes --Yes Yes Bi 2 (InNb)O 7 23 Yes -No Yes Yes Yes (Bi 1.93 Fe 0.07 )(Fe 1.42 Te 0.58 )O 7 49 Yes Yes --Yes Yes Ca 1.46 Ti 1.38 Nb 1.11 O 7 50 No Yes --Yes Yes
42 The relaxation in Bi pyrochlores has been ascribed to the random hopping of among equivalent sites. 45 For most Bi pyrochlores the A site cation is usually displaced from its ideal position to the 96 g when this occurs the re are 6 equivalent positions where the cation can reside in the structure. The hopping mechanism is shown in F igure 2 9 the Bi cation must overcome an energy barrier before transitioning into the lower energy equivalent 96 g site. Figure 2 9 A schematic showing a Bi cation pathwa y hopping between 96 g site 2.5 Vibrational Spectroscopy 2.5.1 Normal m ode d etermination Nuclear site group analysis allows for the determination of the infrared (IR) and Raman active modes in solids without the need of a detailed analysis of the symmetry elements of the unit cell. Using T ables A, B, and E provided by Rousseau et al. 51 along with the space group and Wyckoff positions of each atom of the unit cell one has sufficient information to determine th e selection rules. Table A provides the site symmetries depending on the space group and Wyckoff positions. Table B specifies the
43 lat tice mode for each symmetry and T able E presents whether the modes are Raman active, IR active, silent, or both Raman and I R active. The irreproducible representation ( ) is calculated by the sum of the Raman and IR active modes minus the acoustic modes. 2.5.2 Raman sc attering Raman spectroscopy involves the inelastic scattering of light by a molecule/material. An electric field is generated by an intense light beam that polarizes the electron clouds that make up chemical bonds. By reversing the field the energy stored in the distorted electron cloud is released, and creates a spontaneous emission of photons. The re emitted light is usually of the same frequency as the in cident light (Raleigh scattering), however a small amount of the energy (1 in 10 6 photons) is transferred to the material and sets it into vibration. This results in the emission of light with a frequency shifted lower than the incident light by an amount equal to the vibrational frequency of the target material. In order for a material to be Raman active, the vibration of the crystal must be accompanied with a change in the polarizability of the molecule. 52 2.5.3 Infrared a bsorption There are two important conditions that are critical to the infrared (IR) absorption process: these are the radiation frequency and the molecular dipole moment. Res onance between the radiation and material occurs when the specific oscillating radiation frequency matches the natural frequency of a particular normal mode of vibration. However in order for energy to be transferred from the IR photon to the material via absorption the dipole moment of the molecule must change due to this vibration. 53
44 Raman and Infrared sp ectroscopy are complementary techniques and a lthough some vibrations may be active in both Raman and IR, these two forms of spectroscopy arise from different processes and different selection rules.
45 CHAPTER 3 EXPERIMENTAL PROCEDURES AND PROCESSING 3.1 Bi 2 Ti 2 O 7 Synthesis 3.1.1 Powder s ynthesis To prepare 0.01 mol of Bi 2 Ti 2 O 7 nitric acid (Ricca Chemical Company 35% v/v ) bismuth sub nitrate (Fisher USP 0.05/5 mol ), ammonium hydroxide (Acros Organics, 28 30% solution of NH 3 in water), and titanium (IV) iso propoxide (Acros Organics, 98+%) were used as starting materials. Bismuth sub nitrate (0.02 mol ) was dissolved in nitric a cid (40 mL) after approximately 20 min of stirring. The ammonium hydroxide (40 mL) was kept in a freezer below 0C, while the bismuth ni trate was dissolved. Titanium isopro poxide (0.02 mol plus a 23% excess 54 ) was added to the bismuth nitrate solution followed by 5 min of stirring. The ammonium hydroxide was then poured into this mixture and after vigo rous stirring a white precipitate was formed. The precipitate was filtered, rinsed with abundant DI water, and dried overnight. After the drying process off yellow powder aggregates were ground with a mortar and pestle until a homogenous white fine powder was observed. A calcination step was carried out at 550C for 16 h with a heating and cooling rate of 200C/h in a zirconium oxide crucible. 3.1.2 Pellet f ormation After the powder was calcined the powder was mortar and pestle and sie ved cylindrical pellets with a diameter of 13mm, 7mm, or 3mm with a thickness of approximately 1 mm. The samples were then isostatically pressed at 250 MPa to further increase the density of the green body. The pellets were microwaved sintered in a
46 ThermWAVE 1.3 furnace using silicon nitride susceptors to attain a heating rate of 80C/min and a holding temperature of 1200C for 45 min. The samples were ambient cooled to room te mperature inside the microwave furnace. For dielectric measurements the sintered pellets were polished to a 1200 grit (SiC) finish, sonicated in water for 10 min and then electroded with gold (sputter coated) and silver paste. They were then dried overnig ht at 120C. pellet, where one edge was ~ 1 mm in thickness which tapered to a point on the other end of the pellet (~ 0.1 mm thickness) The slanted face of the p ellet was the n polished 3.2 Solid State Synthesis 3.2.1 Powder s ynthesis All other polycrystalline pyrochlores and Ln 3 NbO 7 were prepared by solid state processing. The starting materials were Dy 2 O 3 (Alfa, 99.99%), Yb 2 O 3 (Alfa, 99.9%) Sm 2 O 3 Sn 2 O 3 Nb 2 O 5 (Alfa, 99.9985%), Gd 2 O 3 (Alfa, 99.99%), TiO 2 and Ta 2 O 5 (Alfa, 99.99%). The powders were mixed in their desired molar ratios and were mixed with 70 ml of deionized water and 2 ml of ammonium polyacrylate dispersant (Dar van 821 A). The milling media contained 60 g of yttria stabilized zirconia spheres with diameters of 10mm and 3 mm, respectively. The slurry was ball milled for 24 hours at 85 rpm. The slurry was then poured onto a Teflon sheet, covered with aluminum foil, and subsequently dried in the oven at 120C for 16 hours followed by grinding with a in an alumina crucible and calcined in air with a 200C/h heating and cooling rate. The
47 ca lcination temperatures and times for the synthesized compositions are presented in Table 3 1. 3.2.2 Pellet f ormation After the phase pure phase was formed, 1wt% 3wt% of PVA binder (Celvol 103) was added to assist in pellet formation. The binder contained 20vol% PVA and 80vol% deionized water. The binder and the powders were mixed with mortar and pestle and 120C for 5 min to evaporate water. The powders were then uniaxially pressed at 150 MPa into cylindrical pellets with a diameter of 13 mm or 7 mm and a thickness of approxi mately 1 mm. The pellets were then isostatically pressed at 250 MPa they were then sintered in a conventional furnace with a heating and cooling rate of 200C. The sintering temperatures and times for the synthesized compositions are shown in Table 3 1. T able 3 1. The calcination and sintering times and temperatures for the solid state synthesized oxides. Compound Calcination Temperature Calcination Time Sintering Temperature Sintering Time Gd 3 Ta O 7 1400C 8 h 1650C 6 h Gd 3 Nb O 7 1400C 4 h 1600C 4 h S m 2 Ti 2 O 7 1250C 9h 1300C 2h Yb 2 Ti 2 O 7 1250C 8h 1250C 10h (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 1250C 8h 1250C 10h (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 1250C 8h 1250C 10h (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 1250C 8h 1250C 10h Dy 2 Ti 2 O 7 1250C 10h 1300C 3h (Sm 0.50 Dy 0.50 ) 2 Ti 2 O 7 1250C 10h 1300 C 2h Sm 2 Sn 2 O 7 1100C 8h 1150C 2h Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 1150C 6h 1200C 8h
48 3.3 Characterization 3.3.1 Structural c haracterization structural characterization. The XRD was conduc operational conditions of 40kV and 20mA for the APD and 40kV and 40mA for the the calcined powders were ground by mortar and pestle. After t he pellets were sintered, XRD was used again to check the phase purity and to ensure no secondary phases were present in the sintered samples. In addition to the above, h igh resolution synchrotron powder diffraction data were collected for Bi 2 Ti 2 O 7 using t he diffractometer at 11 BM at the Advanced Photon Source (APS) 55 Argonne National Laboratory using an average wavelength of 0.413 . Discrete detectors co vering an angular range from 6 to 16 2 are scanned over a 44 2 range, with data points collected every 0.002 2 and scan speed of 0.15/s. The temperature was controlled by an Oxford closed helium cryostat from 5 K to 298 K, the temperatures between 300 K and 400 K were controlled by an Oxford cryostream 700+ N 2 thermal transport between the small diameter kapton capillary and the helium exchange gas. The kapton capillaries were rotated normal to the beam direction all the time during the X ray exposure to avoid sample preferred orientation Neutron diffraction for Bi 2 Ti 2 O 7 was measured by Professor Brendan J. Kennedy at the University of Sydney. A pproximately 7 g of Bi 2 Ti 2 O 7 was used in the high resolution powder diffractometer (Echidna) at the OPAL reactor neutron facility,
49 Australian Nuclear Science and Technology Organization The powdered sample was lightly packed into a vanadium can that was mounted in closed cycle refr igerator with 60 80 mbars of He exchange gas. All diffraction patterns were recorded over the angular range 10 to 160 degrees at a wavelength of 1.494 . A pattern was recorded at 3, 25 and 50 K, then in 15 K steps to 150 K at 200 K, then in 50 K steps t o 400, at 425 then 25 K steps to 550 K, and finally at 565 and 580 K. During all measurements the temperature variation was less than 2 K. 3.3.2 Infrared and R aman c haracterization The IR spectra was measured by Evan Thatcher in Prof group. Temperature dependent reflectivity was obtained using a Fourier transform spectrometer (Bruker IFS 113v) in conjunction with a liquid helium cooled Si bolometer (over 30 700 cm 1 ) and a room temperature DTGS detector (over 650 3300cm 1 ). The reflection stage provided an angle of incidence of about 15 for the light. Temperatures between 20 and 300 K were obtained in a Hanson flow cryostat with polyethylene (far infrared) or KBr windows (midinfrared). Raman measurements were p erformed on a Thermo Scientific DXR Raman microscope system. The Raman shift was measured from 50 to 3500 cm 1 by exciting the sample with a 532 nm photon beam from a 1 mW laser. The spectrometer was equipped with a 900 line/mm filter grating and a 50 m spectrograph aperture. The measurement data was compiled over 10 exposures with 512 background exposures, each taken at room temperature with an exposure time of 2 seconds. 3.3.3 Dielectric c haracterization To prepare parallel plate capacitors, gold el ectrodes were sputtered on both sides of the polished pellets followed by a painted coat of air dried silver paste.
50 The dielectric measurements as a function of temperature were collected with an Agilent E4980A Precision LCR Meter using a computer control led closed cycle cryogenic workstation (CTI Cryogenics, model 22) and a Delta 9023 oven. The measurements were carried out from 20 to 300 K in the former, and from 300 to 500 K in the later in the frequency range between 40 Hz and 2 MHz. Data at higher temperatures (373 723 K) was obtained placing the samples in a quartz tube reactor located inside a tube furnace. The thermocouple was placed in close proximity to the pellets in order to have accurate temperature control. Measurements in the frequency r ange from 1 kHz to 1 MHz were carried out using the Agilent E4980A Precision LCR Meter. Impedance measurements as a function of frequency were collected using a solartron SI 1260 impedance analyser for measurements from 298 K 473 K over the frequency ran g e 0.1 Hz the electrodes using conductive silver paste (SPI Supplies) which was allowed to dry before the samples were installed in a glass reactor for measuring. For impedance measurements from 20 K 300K using a computer controlled closed cycle cryogenic workstation (CTI Cryogenics, model 22) and an Agilent 4294A Precision Impedance Analyzer wi th measurements obtained at 10 K intervals at frequency ranges of 40 Hz to 1 MHz 3.4 Computational Methods The computational calculations discussed in C hapter 6 were performed by Dr. Beverly Hinojosa. First principles calculations were performed with Vienna ab initio Simulation Package (VASP), 56 59 a plane wave density functional theory (DFT) code, using the projector augmented wave (PAW) pseudopotentials provided in the VASP
51 database. 60 61 The Bi(5 d 6 s 6 p ), Ti(3 s 3 p 3 d 4 s ), and O(2 s 2 p ) orbitals were included as the valence electrons. The calculations were performed within the local density approximation (LDA) 62 since it has been found to be more accurate than the GGA functionals for many pyrochlores. 63 64 Electronic relaxation was performed with the conjugate gradient (CG) method accelerated using Methfessel Paxton Fermi level smearing with a Gaussian width of 0.1 eV. 65
52 CHAPTER 4 CRYSTALLOGRAPHY OF Bi 2 Ti 2 O 7 AND OTHER PYROCHLORES 4.1 Introduction The crystallography of regular pyrochlores (A 2 B 2 O 7 ) is well understood. A summary of the different descriptions of the p yrochlore structure wa s presented in Chapter 2. This C hapter will investigate the structure of the (Sm x Yb 1 x ) 2 Ti 2 O 7 Sm 2 (Sn x Ti 1 x ) 2 O 7 and in particular establish whether or not the structures are displaced or ideal pyrochlores. An in depth structural stud y of Bi 2 Ti 2 O 7 will be performed as function of temperature using both neutron and synchrotron x ray diffraction sources. For the first time the structure of Bi 2 Ti 2 O 7 will be refined experimentally and compared to previous density functional (DFT) theory ca lculations. A ccording to Esquivel Elizondo et al., 26 DFT calculations indicate that the atoms within the Bi 2 Ti 2 O 7 crystal do not reside in ideal pyrochlore positions. In Bi 2 Ti 2 O 7 the A cation (bismuth) is displaced from its ideal 16 c (0,0,0) position to the 96 g (0.015, 0.015, 0.964) site. The O(2) atom is also displaced ; instead of res iding in the 8 a site (1/8, 1/8, 1/8) it is displaced to the 48 f ( x 1/8, 1/8) position. Furthermore, previous DFT calculations have ascribed a large isotropic thermal parameter to the Ti cation. 26 This is caused by the bismuth displacement to the 96 g site, which leads to distortion in the Bi O bonding and this loss of symmetry results in a n underbonded Ti atom. In an effort to satisfy this O underbonding the Ti cation is predicted by DFT calculations to displace to the 96 g position; however, it is important to recall that DFT calculations do not take into account thermal considerations. Th e previous DFT calculations assumed stoichiometric bismuth titanate ( i.e full occupancy of the Bi and O(2) sites). Given the improved
53 quality of fit of the neutron diffraction found here with Bi vacancies considered, the DFT calculations of bismuth titan ate were repeated with Bi and O(2) vacancies. 2 Ti 2 O 7 are similar to that observed in another bismuth pyrochlore, Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 (BZN). 1 3 No netheless, what is striking is that displacement would occur without atomic substitutions and multiple site occupancy like in BZN and related pyrochlores. 4.2 Crystal Structure of (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) Pure pyrochlore phase of (Sm x Yb 1 x ) 2 T i 2 O 7 ( x = 0.25, 0.5, 0.75) was formed when calcined at 1250C and sintered at the same temperature (Figure 4 1). The XRD pattern show s no reflections associated with any impurities of any other related superstructures. Figure 4 1. XRD patterns of (Sm 0. 25 Yb 0.75 ) 2 Ti 2 O 7 (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 The lattice parameters were calculated by the Nelson Riley function:
54 (4 1) where a is the apparent lattice parameter, a o is the lattice parameter, and k is a constant. The Nelson riley function is used to correct for the sample displacement error. Table 4 1 lists an example of the cos 2 2 and the apparent lattice based on a single reflection. Table 4 1. The 2 positions, the corresponding (hkl), the cos 2 2 parameter, and the apparent lattice parameter of (Sm 0 .25 Yb 0.75 ) 2 Ti 2 O 7 2 (degrees) hkl cos 2 2 a ( ) 15.25 9 111 7.59520 10.0453 29.268 311 3.98171 10.1083 30.585 222 3.81232 10.1133 35.434 400 3.29666 10.1211 38.711 331 3.02061 10.1269 50.869 440 2.99371 10.1420 53.362 531 2.18986 10.1451 60.416 622 1.92359 10.15144 Figure 4 2 indicates the apparent l attice parameter a vs. cos 2 2 and the resulting a o The lattice parameters, shown in Table 4 2 decrease as the Sm content is decreased, this is expected as Sm has a larger ionic radius than Yb. (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 : y = 10.18425 0.018511 x (Sm 0. 5 0 Yb 0. 5 0 ) 2 Ti 2 O 7 : y = 10.12958 0. 01198 x (Sm 0. 7 5 Yb 0. 2 5 ) 2 Ti 2 O 7 : y = 10.08704 0.01198 x Figure 4 2. Nelson Riley function for the lattice parameter calculations of (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7
55 Table 4 2. Lattice Parameters of (Sm 0. 25 Yb 0.75 ) 2 Ti 2 O 7 (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 Compound Lattice Parameter ( ) (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 10.08704 (Sm 0. 5 0 Yb 0. 5 0 ) 2 Ti 2 O 7 10.12958 (Sm 0.7 5 Yb 0.2 5 ) 2 Ti 2 O 7 10.18425 Structural studies on BZN, a pyrochlore that has atomic displace ments, have shown that an extra peak (corresponding to a 442 hkl) not indexed by the ideal pyrochlore structure will be present in the XRD. This peak is absent in both the powder and the sintered pellets which shows that these compounds do not have atomic displacements, only chemical substitution. 4.3 Crystal Structure of Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 Pure pyrochlore phase of Sm 2 ( Sn x Ti 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) was formed when calcined at 1100C (Figure 4 3). The XRD pattern show no reflections associated with a ny impurities of any other related superstructures. As the Sn content increases in the material some reflections increased decreased in intensity, in particular the (111), (113), and (133) peaks at 15, 29, and 38 respectively. These changes in intensiti es are consistent with the patterns of Sm 2 Sn 2 O 7 and Sm 2 Ti 2 O 7 in both theoretical patterns and those reported in literature. 66 The Sm 2 (Sn x Ti 1 x ) 2 O 7 powders were then sintered at 1300C, however both Sm 2 (Sn 0.25 Ti 0.75 ) 2 O 7 and Sm 2 (Sn 0 .75 Ti 0.25 ) 2 O 7 showed the presence of impurity peaks, while Sm 2 (Sn 0. 5 Ti 0.5 ) 2 O 7 sintered at the same temperature resulted in a phase pure pyrochlore.
56 Figure 4 3 XRD patterns of Sm 2 ( Sn 0.25 Ti 0.75 ) 2 O 7 Sm 2 ( Sn 0. 5 Ti 0.5 ) 2 O 7 and Sm 2 ( Sn 0.7 5 Ti 0.2 5 ) 2 O 7 Similar to the (Sm x Yb 1 x ) 2 Ti 2 O 7 system, the Sm 2 (Sn x Ti 1 x ) 2 O 7 system does not have the presence of the (442) peak which indicates that there is no evidence of atomic displacement in the material. 4.4 Structural Study of Bi 2 Ti 2 O 7 Table 4 1 shows the r efined positions and parameters of the neutron, HR XRD, and DFT calculations performed in the following subsections.
57 Table 4 3 Refined positions and parameters of Bi 2 Ti 2 O7 at 3 K through neutron diffraction ( a ), high resolution XRD ( b ), non stoichiometric Bi 1.8125 Ti 2 O 6.75 DFT calculations ( c ), stoichiometric DFT calculations ( d ) a ( ) 10.3310 a 10.346 10.335 0.005 c 10.335 0.005 d Atom x y z B iso ( ) Occupancy Bi 96 g 0.0166 a 0.0166 a 0.9707 a 1.11 a 0.075 a 0.0181 0.0181 0.971 0.0 11 0.1694 0.015 c 0.015 c 0.964 c 1.88 c 0.0755 c 0.015 d 0.015 d 0.964 d 0.079 d 1/6 d Ti 16 d 0.5 a 0.5 a 0.5 a 0.60 a 0.083 a 0.5 0.5 0.5 0.008 1 0.5 c 0.5 c 0.5 c 2.41 c 0.0833 c 0.5 d 0.5 d 0.5 d 1.82 d 1 d O(1) 48 f 0.4312 a 0.125 a 0.125 a 0.92 a 0.25 a 0.433 0.125 0.124 0 .018 1 0.431 c 0.125 c 0.125 c 2.21 c 0.25 c 0.431 d 0.125 d 0.125 d 0.800 d 1 d O (2) 8 a 0.125 a 0.125 a 0.125 a 2.66 a 0.031 a 48 f 0.145 0.125 0.125 0.003 0.1688 0.431 c 0.125 c 0.125 c 2.21 c 0.25 c 0.136 d 0.125 d 0.125 d 0.237 d 1/6 d 4.4.1 Synchrotron X ray d iffraction The synchrotron powder X ray diffraction pattern (SXRD) recorded for the sample of Bi 2 Ti 2 O 7 is illustrated in Figure 4 1 and the refinement is shown in F igure 4 2 together with the best Rietveld fit. Attempts to model the data with the Bi at t he 16 c site ( 0 0 0) resulted in an unacceptably high 2 value of 8.24 and Bi displacement parameter U iso (Bi) = 0.0694(3) 2 High displacement parameters are commonly associated with vacancies R efinements where the Bi occupancy was also varied resulted in a small improvement in 2 to 7.37 but did not significantly reduce the value of U iso (Bi) = 0.0667(3) 2 with the Bi stoichiometry being reduced from 2.00 to 1.64(5). Examination of the Rietveld difference profile revealed a num ber of discrepancies t herefore disorder of the Bi cation was considered The f in al fit illustrated in Figure 4 2 allows the Bi to displace to the 96 g sites and yielded 2 to 2.15 with U iso (Bi) = 0.0117(3) 2 The Bi
58 stoichiometry was estimated to be 1.70(1). Note that no ab sorption correction was applied to the SXRD data. Figure 4 4 High resolution XRD at temperatures from 6 k to 250 K. Inset is the (111) peak at 8. The possibility that the Bi was dis placed to the 96 h sites was also investigated This resulted in a c ompar able quality fit to the data but it was not possible to distinguish between these by diffraction methods alone. Whilst disorder onto the 96 h and 96 g sites are not crystallographic equivalent descriptions they both describe displacement of th e Bi cati on away from the center of the O(1) to a 6 site puckered hexagon.
59 Figure 4 5 Rietveld fit of the room temperature x ray diffraction pattern. Only peaks ascribed to the cubic pyrochlore phase were detected. Unlike the neutron diffraction, the high r esolution XRD did not display a low temperature saturation in the lattice parameter below 150 K (Figure 4 3 ). In summary the SXRD data clearly demonstrates there to be appreciable non correlated atomic displacements of the Bi cation, and suggest the Bi mo ves around 0.4 away f r om the position it would occupy in the ideal pyrochlore structure. Given the large X ray scattering power of the heavy Bi cations the refinements were insensitive to either disorder of the other ions or the possibility of vacancies on the O(2) sites. Such vacancies are required to charge balance.
60 Figure 4 6 The lattice parameter between 6 K and 150 K, unlike in neutron diffraction a low temperature saturation is not observed. 4.4.2 Neutron d iffraction All the reflections obse rved in a powder neutron diffraction pattern collected for Bi 2 Ti 2 O 7 at room temperature using 1.622 neutrons could be indexed to a cubic cell in with a = 10.3410(2) . No evidence was found for any spurious peaks in the pattern and it was conclud ed that the material was single phase. Data were then collected between 3 and 580 K using 1.494 neutrons. These patterns showed some weak reflections due to parasitic scatter from the cryostat and these were treated as excluded regions in the subsequen t structural refinements (Figure 4 4) A second feature of the patterns was the presence of some structure in the background. This additional diffuse scattering is indicative of some short range disorder in the structure, possibly associated with the ani on sub lattice. Examination of the SXRD data also
61 revealed some very weak diffuse character this behavior was weaker in the SXRD pattern than in the ND is consistent with this being caused by anion disorder. As described above fitting the room temperatur e neutron diffraction pattern to the ideal pyrochlore structure yielded unusually large displacement parameters for the Bi cations, 5.3(1), suggesting the possibility of substantial non correlated atomic displacements Figure 4 7 Rietveld fit of the room temperature neutron diffraction pattern. Only peaks ascribed to the cubic pyrochlore phase were detected. It is well established that the Bi cations, located at the center of a distorted scalenohedron of 8 anions are susceptible to disorder. Recent crystallographic studies of Bi 2 x Yb x Ru 2 O 7 and Bi 2 CrTaO 7 have demonstrated the static non correlated atomic displacements of the Bi cations from the 16 c (0 0 0 ) site to a 96 h (0 y y) site occurs in
62 Bi pyrochlores. Allowing for disorder of the Bi catio n lead to a significant improvement in the fit and a noticeably reduction in the magnitudes of the refined displacement parameters for the Bi cations, although it did not substantially change the refined value of the unknown x parameter of O(1) (from 0.433 0(2) to 0.4310(1)). The possibility of vacancies at the Bi site was investigated and the addition of this parameter led to a significant improvement in the quality of the fit. Bi vacancies have been observed in a number of other pyrochlores including Bi 1.89 Ru 2 O 6.92 Bi 1.89 GaSbO 6.84 and Bi 1.95 Rh 2 O 6.83 Refinement of the occupancy of the O(2) site demonstrated this was not fully occupied; and in the final refinement cycles the occupancies of the Bi and O(2) sites were constrained to maintain charge neutral ity. As noted by Avdeev et al., 67 displacement of the Bi away from the 16 c sites is expected to forc e the O(2) atoms away from the 8 a (1/8 1/8 1/8) sites to a disordered 32e (x x x) site. Attempts to verify this were inconclusive using the neutron results but are taken into consideration for the DFT work Finally the possibility of disorder of the Ti c ations was considered. Although stable refinements could be obtained if the Ti was disordered to (x x y) these invariable resulted in physically unrealistic displacement parameters for the Ti cations and we conclude that any such disorder must be localize d. The temperature dependence of the lattice parameter, is illustrated in F igure 4 5 shows normal thermal expansion behavior at high temperatures and saturation effects as the temperature approaches 0 K. The behavior was well modelled by fitting to a fun ction of the form: 6 1
63 The temperature, included to account for the low temperature saturation of thermal expansion was estimated to be ~ 210 K. This is somewhat higher than the value typically seen for thermal expan sion of oxides such as perovskites. Figure 4 8 Temperature dependence of the lattice parameters of Bi 2 Ti 2 O 7 Where not apparent the effective standard deviations are smaller than the symbols. The solid lines is a fit to E quation 6 1 4.4.3 DFT c alculations The Bi displacements and the resulting change in the positional parameter for O(1) observed from neutron diffraction (summarized in T able 4 1 ) are in excellent agreement with the recent predictions for stoichiometric bismuth titana te from DFT. 26 As previously stated, the O(2) atoms are located at the ideal 8 a position with a large isotropic thermal parameter of 2.66 according to the neutron work. In stoichiometric DFT calculations O(2) was found to displace to the 48 f (0.136, 1/8, 1/8) position, which corresponded to a displacement of approximately 0.11 towards the
64 edges of the Bi 4 O tetrahedra. The large isotropic parameter r eported here for O(2) by neutron diffraction corresponds to an average thermal displacement of 0.18 which is greater than the displacement magnitude predicted by stoichiometric DFT calculations The stoichiometric DFT calculations also predicted a dis placement of Ti from the high symmetry site in order to satisfy the bond valence for O after Bi displacement. However, with the lack of experimental evidence the Ti displacement was explained as Ti centered at the high symmetry site with an isotropic ther mal parameter B iso =1.82 In comparison with the isotropic thermal parameter from neutron diffraction reported in T able 4 1 the ellipsoid of the Ti in the stoichiometric bismuth titanate predicted by DFT is more than double the size based on the neutron diffraction reported here. The A 1x1x2 supercell was created to provide more flexibility in the possible stoichiometry configurations Following optimizations, the resulting atomic positions are also included in T able 4 1 There are two major differe nces between the previously reported structure and that found here by DFT the nonstoichiometric calculations First, the isotropic displacement parameters are considerably larger for the nonstoichiometric calculations This is because there were signifi cant local effects due to the vacancies. Specifically, the Bi and O(2) displacements were substantially larger isolated near a vacancy. It was found that near a vacancy the atomic displacement magnitude could be nearly double that away from a vacancy. S ince neutron diffraction averages over a sample containing many unit cells, the atomic positions from the DFT calculations were averaged as well. This averaging results in larger isotropic thermal parameters than those reported for the stoichiometric struc ture and those determined from neutron diffraction. This is not unexpected given that the Bi and O(2) atoms will
65 displace to help compensate for the loss of bonding due to the inclusion of vacancies. Specifically, a Bi cation located at an O(2) vacancy w ill need to bond more strongly with the remaining O(2) anion as well as the six O(1) forming the puckered ring perpendicular to the O(2) Bi O(2) bonding axis. This will result in an increased displacement of the Bi and the O(2) atoms. Also, through a sec ondary effect, the Ti and O(1) atoms will also be affected by the vacancies as seen by the large isotropic thermal parameters for both in T able 4 1. Secondly, and for the same reasons, the displacement of the O(2) atom was larger here. Again the displacem ent magnitude was considerably larger near vacancies and this led to a larger x parameter identified here versus the stoichiometric DFT simulation. Additionally, given the large isotropic parameter for O(2) even after displacement, attempts were made to ce nter the O(2) at the 32e position but the resulting isotropic parameter was larger at 3.67 and the actual displacement of the O(2) atoms was not accurately captured. The change in Gibbs free energy for the non stoichiometric and stoichiometric Bi 2 Ti 2 O 7 str ucture was defined as the vacancy formation energy in electron volts (eV). The total energy change due to atomic displacements at room temperature is 1.925 eV, while the vacancy formation entropy is 3.13 eV at room temperature. The inclusion of oxygen vac ancies costs considerable energy when compared with the favourable energy change due to atomic displacements. Other oxides, such as SrTiO 3 and BaTiO 3 have a vacancy formation energy of 6.88 eV 68 and 2.0 eV 69 respectively. By comparing the vacancy formation energy, an oxygen vacancy is more favorable in Bi 2 Ti 2 O 7 than in SrTiO 3 but less favorable than in BaTiO 3
66 4.5 Conclusion The struc tural characterization of (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 (x = 0.25, 0.5, 0.75) was presented here. It was found that both systems formed a phase pure pyrochlore phase and the presence of the (442) diffraction peak was not detected. Therefore, both o f the Sm systems only have the presence of substitution and do not have atomic displacements found in most Bi pyrochlores. A more in depth structural study of Bi 2 Ti 2 O 7 was performed using neutron diffraction, synchrotron x ray diffraction (SXRD), and DFT. Both the neutron and SXRD revealed displacements of the Bi cation to the 96 g oxygen. The neutron and SXRD both showed a better fit when vacancies were considered on the Bi and O(1) site, the energy of formation of non st oichiometric Bi 2 Ti 2 O 7 was found to be 3.13 eV at room temperature. 2 Ti 2 O 7 are similar to that observed in another bismuth pyrochlore, Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 (BZN). 1 3 Nonetheless, what is striking is that displacement would occur without atomic substitutions and multiple site occupancy like in BZN and related pyrochlores.
67 CHAPTER 5 DIELECTRIC PROPERTIES OF Bi 2 Ti 2 O 7 AND OTHER PYROCHLORES 1 5.1 Introduction Over the last decades, extensive research has been done in order to explain a phenomenon that is common to several pyrochlores and all Bi pyrochlores: a temperature and frequency dependent dielectric r elaxation consistent with glass like dipolar mechanisms. 12 22 23 45 70 71 On cooling below room temperature, these materials exhibit a step like decrease in the real par t of the dielectric permittivity accompanied by a broad frequency dependent peak in the imaginary part. As a consequence of this relaxation, at microwave frequencies the temperature at which the dielectric loss peaks (T m ), move towards room temperature wi th increasing frequency as observed in Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 thus limiting GHz frequency applications. 2 [It is important to note that this pyrochlore is not fully stoichiometric as previously demonstrat ed, but it is usually reported with nominal composition Bi 1.5 Zn 1.0 Nb 1.5 O 7 (BZN). 12 45 ] Several potential explanat ions for the observed relaxation in Bi pyrochlores have been proposed including the hopping of the disordered cations at the A equivalent sites, 12 reorientation of unstable dipoles due to interactions in the A 2 structure, 72 and chain rotation modes. 23 Furthermore, until recently, it was considered that chemical disorder (more than one cation species sharing the A or B sites), highly polarizable lone pair cations such as Bi 3+ and atomic displacements are responsible for the relaxa tion behavior. However, our work on calcium titanium niobate 73 proved that pyrochlores can exhibit dielectric relaxation even in the absence of a highly polarizable A site cation or a 1 Adapted from Christopher Turner et. al. Dielectric properties and relaxation of Bi 2 Ti 2 O 7 Journal of the American Ceramic Society doi:10.111/jace.12803 (2014).
68 lone pair element. As such, the measurement of the dielectric properties of Bi 2 Ti 2 O 7 a cubic pyrochlore without substitutions on both the A and B site, is extremely desirable because this compound could help isolate the possible causes and aid in determining the necessary and sufficient conditions for the observed dielectric r elaxation. Bismuth titanate is expected to have dielectric relaxation as calculations employing density functional theory (DFT) have demonstrated the possibility of atomic (ionic) jumps among equivalent crystallographic positions associated with a low ac tivation energy. 74 If this prediction is confirmed, this would mean that non correlated atomic displacements are a necessar y condition for relaxation. Even if there is no typical dielectric relaxation observed the absence of relaxation can prove that substitutional cations would be a required condition for dielectric relaxation in pyrochlores. In order to isolate the effect of substitutional cations on dielectric relaxation (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 ( x = 0.25, 0.5, 0.75) were synthesized. The appearance of relaxation in these compounds would prove that substitutional cations are sufficient for dielectric relaxation In this C hapter the dielectric properties of Bi 2 Ti 2 O 7 (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) and Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 are comprehensively studied as a function of temperature and frequency in order to clarify the presence of relaxation in this material, and in turn, better understand the nature of the dielectric rela xation phenomenon observed in pyrochlores.
69 5.2 Dielectric Analysis of Bi 2 Ti 2 O 7 5.2.1 Dielectric a nalysis as a function of t emperature The measured relative permittivity at 100 kHz and 298 K w (dielectric loss) was 0.0064. The o btained dielectric permittivity is in agreement with simil ar bismuth pyrochlores such as BZN that has a permittivity of 150 and tan delta of <0.008. The values for the real and the imaginary parts of t he dielectric permittivity as a function of temperature and fixed frequency are illustrated in F igure 5 1A for BZN (the result of re measuring a sample from previous work ), 3 and in F igure 5 1 B for Bi 2 Ti 2 O 7 The dielectric behavior of BZN is characteristic of Bi pyrochlore s, i.e., a low temperature frequency dispersive dielectric relaxation is observed where T m the temperature where the is at a maximum value for a specific frequency range, shifts to higher temperatures with increasing measuring frequency. Also, the loss value at T m and the width and magnitude of the loss peak increases with increasing frequency. In addition, above T m the dielectric permittivity of BZN at different frequencies seems to converge to the same value as temperature is increased. However, bismuth titanate, despite being a Bi pyrochlore, does not have the same behavior. Even though it is clear that near r oom temperature the relative permittivity of Bi 2 Ti 2 O 7 appears to reach a broad plateau or maximum (except at low frequency as seen at 10 kHz), it is not accompanied by a response in the imaginary part as in the case of BZN. This points to the possibility of a phase transition being responsible for the permittivity change in Bi 2 Ti 2 O 7
70 A B Figure 5 1. The real and imaginary part of the dielectric permittivity as a function of temperature from 10 kHz of A) BZN and B) Bi 2 Ti 2 O 7 A similar phenomenon is observed in Gd 3 NbO 7 a dielectric with a weberite type structure, an anion deficient fluorite superstructure, similar to the pyrochlore structure. 75 The measuremen t was extended up to 483 K looking for indications of dielectric relaxation but was not observed. From F igure 5 1B it is evident that the dielectric permittivity of Bi 2 Ti 2 O 7 at different frequencies does not converge to a common value as in BZN. At 10 kH z (the lowest frequency in F igure 5 1B ) the onset of a peak in the imaginary part is observed but the increasing conductivity prevents further analysis. Therefore, another measurement was carried out including frequencies as low as 80 Hz. The resulting p lot is depicted in F igure 5 2 From this plot it is evident that at low frequencies (<10 kHz) a type of dielectric relaxation is taking place. Nonetheless, the shape of the loss curves does not follow the observed pattern in BZN, specifically, in Bi pyro chlores the loss peaks appear at the same low temperature, which is not the case for Bi 2 Ti 2 O 7 suggesting a different origin for the relaxation. Furthermore, given the low frequency driving the phenomenon, it is most likely indicative of space charge pola r ization
71 Figure 5 2. Imaginary and real part of the dielectric permittivity as a function of temperature from 80 Hz to 2 MHz. To explore the possibility of phase transition as the reason for the dielectric response, differential scanning calorimet ry (DSC) was performed on a Bi 2 Ti 2 O 7 sample from 2 to 200 K. The low temperature DSC did not reveal a phase transition. It is important to note that detailed structural studies of BZN have not revealed any phase transition 2 and therefore the lack of a transition for Bi 2 Ti 2 O 7 is not surprising. Back on the dielectric response presented in F igure 5 2 it is worth mentioning that despite the diffuseness in T m, the relaxation in Bi 2 Ti 2 O 7 where the dielect ric permittivity begins to decrease, occurs at relatively higher temperatures than in BZN (and many other Bi pyrochlores studied so far). Employing the Arrhenius E quation, the Debye model corresponding to a single relaxation time was followed to fit the da ta and determine the activation energy (E a ) and 0 ) of the relaxation phenomenon in Bi 2 Ti 2 O 7 :
72 (5 1 ) r is the frequency of the relaxation peak in the imagi nary part of the permittivity, and k B is the Boltzmann constant. The relaxation behavior was found to follow the Arrheni us E quation quite well (F igure 5 3 ). The calculated activation energy was 0.162 eV (equivalent to 1881.3 K). It is simply anecdotal t o note that this value is in agreement with calculated values from DFT (0.11 0.21 74 ) and is similar to that of BZN (0.136 eV 13 0.202 eV 12 ). However, the attempt jump frequency (9.91 x 10 5 Hz = ~1 MHz) is several orders of magnitude lower (10 12 Hz), which makes the comparison of activation energies pointless since different relaxation mechanisms are likely taking place. Figure 5 3. Arrhenius plot of Bi 2 Ti 2 O 7 dielectric relaxation usi ng Eq uation 5 1. As previously stated, the low attempt jump frequency suggests the presence of space charge polarization within the grain boundaries or an interaction between the
73 surface of the sample and the electrode. Nonetheless, and for the sake of a rgument, if one were to assume that the observed phenomenon is a typical dipolar (ionic) dielectric relaxation; such low frequency would imply the involvement of a large vibrating mass or a cooperative displacement in the form of rigid unit modes. 76 77 Recalling, in BZN the characteristic frequency in the order of 10 12 Hz is normally attributed to the attempt jum p frequency of the hopping of A ions within the A 2 substru cture that is governed by the O phonon vibration. 45 If a rough calculation is used considering harmonic oscillators (m 2 /m 1 1 2 2 2 ), a mass difference of 12 orders of magnitude is obtained between BZN and Bi 2 Ti 2 O 7 In that case, the low frequency dielectric relaxation in Bi 2 Ti 2 O 7 requires a vibrating mass in the order of ~ 5 x 10 10 unit cells, which means that cooperative displacement would be occurring. Given this unlikely event, space charge polarization in the form of hopping or interfacial polarization is clearly more reasonable and it is thus the mechanism here proposed for the observed phenomenon in Bi 2 Ti 2 O 7 It is well known that the electrode diele ctric interface can also lead to electrode polarization relaxation processes. Therefore, in order to verify this possibility (i.e. interaction between the electrodes and the sample), three different electrodes were used for the dielectric analysis, silver paste, platinum ink and gold (sputter coated). In all three cases the same dielec tric response was obtained (F igure 5 1B ). In addition, current voltage tests revealed similar curves with a near linear behavior of positive slope with increasing voltage t hat rules out the possibility of Schottky barriers. 78 79 A high temperature (400 600K) analysis of the dielectric permittivity and loss was carried out to investigate the possibility of a high temperature dielectric relaxation event with the results shown in F igure 5 4 X ray diffraction was performed before and after
74 the high temperature tests and verified that Bi 2 Ti 2 O 7 did not undergo a phase change during testing. Figure 5 4. Imag inary and real part of the dielectric permittivity as a function of temperature at 80, 100, 500 and 1000 kHz. No sign of relaxation was found in the imaginary part; however, there is a clear change in the relative permittivity around 512 K (as mentioned b efore, there are no noticeable features in the calorimetry data at this temperature). It is noteworthy that at 1 546 K, and finally to 0.0317 at 646 K where conductivity i s evident. Furthermore, the dielectric permittivity ranges from 113.59 at room temperature to 122.85 at 646 K. 5.2.2 Dielectric a nalysis as a f unction of f requency Frequency dependent properties of materials are commonly described using 4 main form factor admittance (Y), and complex modulus function (M). These functions are related as follows:
75 (5 2 ) (5 3 ) (5 4 ) (5 5 ) where is the angular frequency ( ), C c is the geometric capacitance and 80 When a single relaxation process is occurring the dielectric response can be modeled by various relaxation models including the Debye relaxation, 44 the Cole Cole relaxation, 81 the Davidson Cole relaxation, 82 and the Havriliak Negami relaxation. 83 Using the relationships in Equations 5 2 5 5 and the relaxation model relationships, all of the dielectric functions will result in semicircles when plotted in the complex plan e. However, depending on the strength of the relaxation not all of these features are experimentally observed. 84 As shown in the work by Cao and Gerhardt 85 conductivity will result in M Z , where is the relaxation time of the specific dielectric function, therefore both the and the peaks will overlap throughout the entire frequency range, thereby giving a clear indication that conductivity is occurring, Bi 2 Ti 2 O 7 does not e xhibit this behavior. In F igure 5 5 the displays a clear peak at 290K while does not over the same frequency range. Due to the unusual nature of the dielectric response of Bi 2 Ti 2 O 7 one can attempt to differentiate conduction and relaxation using frequency dependent plots of the electric modulus, impedance, admittance, and dissipation factor shown in F igure 5 5
76 A B C D Figure 5 5. Frequency plots at varying tem peratures of A ) B) C ) and D ) The imaginary par t of the permittivity is plotted ( F igure 5 5A ) as a function of frequency where it is evident that at temperatures below 150 K no clear dielectric loss peak is observed. Above 150 K, a peak in the dielectric loss becomes clearer, and by 290 K the plot displays the typical peak shape for relaxation fully contained in the frequency range plotted ( F igure 5 6 ).
77 Figure 5 6. Normalized functions of , and at 290 K s ) also exhibit two plateau s visible in the real part of the dielectric permittivity ( r ) versus frequency plot as depicted in F igure 5 7 for Bi 2 Ti 2 O 7 By analyzing the dielectric functions as a function of frequency it is clearly evident that a relaxation event is occurring in Bi 2 Ti 2 O 7 Both and display peaks at similar frequencies, while and do not. The real component of the dielectric permittivity also displays an increase in permittivity with two visible plateaus at temperatures greater than 200 K. This step like increase in permittivity ( r ) along with the peak behavior of prove that relaxation is occurring. 84 However, what makes Bi 2 Ti 2 O 7 different from a typical relaxor dielectric ceramic, such as BZN, is that the relaxation occurs at frequencies below 10 4 Hz which is generally ascr ibed to the space charge polarization mechanism. 86
78 Figure 5 7. Frequency dependent plot of the real part of the dielectric permittivity. So far it seems that the phenomenon is related to space charge polarization rather than dipolar or ionic as seen in BZN. As such, the dielectric study of Bi 2 Ti 2 O 7 makes it evident that chem ical substitution affects the relaxation mechanisms of Bi pyrochlores. For those with substitution on both sites (A and B) similar activation energies and characteristic frequencies have been calculated from the Arrhenius E quation (0.112 0.259 eV and 10 12 10 15 Hz 22 45 72 87 88 ); nevertheless, pyrochlores with substitution only on the B site show different values than the previous group (0.319 0.559 eV and 10 16 10 20 Hz 21 23 ). The values for the attempt jump frequencies for these compounds are clearly unrealistic and thus the authors had to use fitting models with less or no physical meanin g to describe the dielectric behavior. By contrast, bismuth titanate a compound without chemical substitution (substitutional disorder), has an activation energy that fits well in the first group,
79 0 differs orders of magnitude than any oth er Bi pyrochlore and thus it cannot be considered an equivalent (dipolar) dielectric relaxation. Further, as stated before, the recent observation of dielectric relaxation in the Ca Ti (Nb,Ta) O pyrochlores 89 discards the presence of lone pair electrons or highly polarizable cations such as Bi 3+ as necessary conditions for the emergence of the phenomenon. Nevertheless, atomic displacements and substitutional cations are present in those Ca pyrochlores. Remarkably, in this work the dielectric analysis of Bi 2 Ti 2 O 7 has revealed that combined atomic displacements and high polarizability of the A site are not enough to lead to the onset of dielectric relaxation, consisten t with dipolar or ionic mechanism as seen in Bi pyrochlores. This result in combination with the observations in Ca pyrochlores suggests that substitutional cations play an essential role in the emergence of relaxation behavior in these compounds. 5.3 Die lectric properties of the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 system Dielectric characterization of Bi 2 Ti 2 O 7 showed that substitutional cations play an essential role in the emergence of dielectric relaxation in pyrochlores. In order to isolate the effec t of substitutional cations on dielectric relaxation (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 ( x = 0.25, 0.5, 0.75) were synthesized. Chapter 4 showed that both systems do not have atomic displacements, therefore only the effects of A site and B site substitu tion will be studied in order to better understand the nature of the dielectric phenomenon observed in pyrochlores. 5.3.1 Dielectric a nalysis of (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) Dielectric measurements were performed on the (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25 0.5, 0.75) system in order to investigate the effect of substitution on the A site without atomic displacements. The measured relative permittivity at 1MHz and 25C ranges from 54.3
80 59.8, with increasing x 0.00018. The obtained dielectric permittivity is lower than the value of Bi 2 Ti 2 O 7 but this can be attributed to the lack of a highly polarizable A cation such as Bi 3+ As the Yb content decreased the permi ttivity increased, due to the higher polarizability of Sm, while the loss values stayed constant throughout ~ 0.1. The values for the real and the imaginary parts of the dielectric permittivity as a function of temperature and fixed frequency of (Sm x Yb 1 x ) 2 Ti 2 O 7 ( x = 0.25, 0.5, 0.75) are illustrated in F igure 5 7 A C. A B C Figure 5 8 Imaginary and real part of the dielectric permittivity as a function of temp erature from 10kHz to 2 Mhz of A) (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 B) (Sm 0.50 Yb 0.50 ) 2 Ti 2 O 7 and C) (S m 0.75 Yb 0.25 ) 2 Ti 2 O 7
81 The (Sm x Yb 1 x ) 2 Ti 2 O 7 compounds all have a similar dielectric response; the permittivity increases as temperature decreases and the loss remains relatively constant throughout the whole temperature range. (Sm x Yb 1 x ) 2 Ti 2 O 7 compounds do n ot exhibit the typical Bi relaxation behavior seen in BZN and other Bi pyrochlores. Therefore atomic substitution on the A site without atomic displacements is not sufficient for dielectric relaxation in pyrochlores. 5.3.2 Dielectric a nalysis of Sm 2 (Sn 0.5 T i 0.5 ) 2 O 7 Dielectric measurements were performed on Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 i n order to investigate the effect of substitution on the B site without atomic displacements. The was 0.00249. The obtained dielectric permittivity is lower than the value of Bi 2 Ti 2 O 7 but this can be attributed to the lack of a highly polarizable A cation such as Bi 3+ The values for the real and imaginary parts of the dielectric permittivity as a fu nction of temperature and fixed frequency are shown in Figure 5 8. Figure 5 9 Imaginary and real part of the dielectric permittivity as a function of temperature from 10 kHz to 2MHz of Sm 2 (Sn 0.5 Ti 0.5 )O 7
82 Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 does not exhibit the typi cal pyrochlore dielectric relaxation response. Instead, Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 the permittivity remains relatively constant as temperature decreases and the loss remains relatively constant throughout the whole temperature range. Therefore atomic substitution on the B site without atomic displacements is not sufficient for dielectric relaxation in pyrochlores. 5.4 Conclusion A dielectric analysis of Bi 2 Ti 2 O 7 ceramic, a bismuth pyrochlore without substitutional disorder, revealed considerable differences with r espect to the common dielectric behavior exhibited by this family of compounds. The dielectric relaxation observed in BZN is absent in Bi 2 Ti 2 O 7 ; however, a relaxation of a different nature was found at low frequencies (<10 kHz) and at relatively high temp erature (125 K) in Bi 2 Ti 2 O 7 The calculated activation energy and characteristic frequency of this behavior using the Arrhenius model were 0.162 eV and ~1 MHz, respectively. The low attempt jump frequency is consistent with space charge polarization and not the result of dipolar or ionic disorder. The relaxation behavior at low frequency was confirmed with a study The atypical dielectric response of Bi 2 Ti 2 O 7 suggests that substitutional cations (rather than ionic displacements, or lone pair electrons), play a major role in the origin of the dielectric relaxation in pyrochlores. A dielectric analysis of the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 ( x = 0.25, 0.5, 0.75) sys tems, pyrochlores without atomic displacements, revealed no evidence of dielectric relaxation to that observed in BZN. These responses suggest that substitutional cations on their own are not sufficient to induce dielectric relaxation in pyrochlores.
83 CHAPT ER 6 RAMAN AND IR PROPERTIES OF Bi 2 Ti 2 O 7 6.1 Introduction R ecall from C hapter 2 that in the ideal pyrochlore structure (A 2 B 2 O 7 space group, origin 1), the A cation resides at the 16 c site, the B cation at the 16 d site, O at the 48 f site, and the se a position. However, density functional theory (DFT) calculations by Esquivel Elizondo et al. 26 indicate that the atoms within the Bi 2 Ti 2 O 7 crystal do not reside at the ideal pyrochlore positions. Rather, in Bi 2 Ti 2 O 7 the A cation (bismuth) is not located in its ideal 16 c (0,0,0) but is in th e 96 g pyrochlore position: instead of residing in the 8 a site (1/8, 1/8, 1/8), it is displaced to the 48 f ( x 1/8, 1/8) position. Furthermore, a noteworthy feature of the theoretical (DFT) study is a large isotropic thermal parameter ascribed to the Ti cation in the 16 d position. 2 6 This was reported to be the result of the displacement of the bismuth atom towards the 96g site which in turn causes a separation between the regularly symmetric Bi and O atoms, thus resulting in an under coordinated Ti atom. In an effort to satisfy t his O under coordination the Ti cation is predicted by DFT calculations to displace to the 96 g position. To reconcile this rather unprecedented prediction, it is important to recognize that DFT calculations do not take into account thermal considerations (since calculations are performed at 0 K) and that experimental diffraction (X ray and neutron 90 ) experiments to date have not yielded evidence of Ti shifting from the 16d position to the 96g.
84 Therefore, in the past, a large thermal isotropic p arameter has been ascribed to the Ti cation instead of reporting a displacement towards 96g positions. 2 Ti 2 O 7 are similar to those observed in another bismuth pyrochlore, Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 (BZN). 1 3 Nonetheless, what is striking is that this displacement would occur without atomic substitutional atoms (e.g. Bi, and Zn in the A sit e) and multiple site occupancy (e.g. Zn in both A and B sites, both of which are always present in BZN and related pyrochlores. To understand further the implication of the atomic displacements on the local atomic structure and predicted phonons, T abl e 6 1 displays the factor group analysis for Table 6 1. Optical modes for Bi 2 Ti 2 O 7 Distribution of Degrees of Freedom Acoustic Modes Optical Modes Selection Rules Bi Ti O 96 g 16 d 48 f 48 f A 1g 2 0 1 1 0 4 Raman A 1u 1 0 0 0 0 1 Silent A 2g 1 0 0 0 0 1 Silent A 2u 2 1 1 1 0 5 Silent E u 3 1 1 1 0 6 Silent E g 3 0 1 1 0 5 Raman F 1g 4 0 2 2 0 8 Silent F 2g 5 0 3 3 0 11 Raman F 1u 5 2 3 3 1 12 Infrared F 2u 4 1 2 2 0 9 Silent 4A 1g (R)+A u ( )+A 2g ( )+5A 2u ( )+6E u ( )+5E g (R)+8F 1g ( )+12F 1u (IR)+11F 2g (R)+9F 2u ( )
85 Bi 2 Ti 2 O 7 following the DFT positions by Esquivel Elizondo et al. 26 The irreproducible representation ( ) was derived using the normal mode determination tables. 51 Using Schnflies notation, the space group for Bi 2 Ti 2 O 7 is ; bismuth has a poin t group symmetry representing a cyclic point group with a two fold rotation, while titanium has a dihedral point group symmetry with a three fold rotation and 3 two fold axes perpendicular to the three fold axis and a horizontal mirror plane. Both O represented by the point group symmetry which is a cyclic group with a two fold rotation and 2 vertical planes. Recalling that in the ideal pyrochlore structure the factor group analysis yields 91 : 3A 2 u +3E u + A 1 g (R) + E g (R) + 4F 2 g (R) + 8F 1 u (IR) +4F 2 u +2F 1 g ( 6 1 ) In the proposed Bi 2 Ti 2 O 7 structure the anticipated modes, following normal coordinate analysis methods, are: 4A 1g (R) +A u +A 2g +5A 2u +6E u + 5E g (R) +8F 1g + 12F 1u (IR) + 11F 2g (R) +9F 2u (6 2) When compared to the ideal pyrochlore structure, one can expect more F 1 u infrared active (IR) modes to appear in the spectra. It is also important to note that in both Equation 5 1 and Equation 5 2 the acoustic mode has been subtracted from the total number of vibrational modes. Furthermore, it has also been proposed by Chen et al. 92 that disorder in the A site leads to a break in the selection rules and, therefore, the normally IR active low frequency modes, such as F 1u may also appear in the Raman spectra. Atomic (valence) force field analysis allows for the identificat ion of the type of interactions that contribute to each phonon mode. It also provides an insight into the structure of a cell by comparison with similar crystals, such that atomic disorder can be discerned. This has been previously demonstrated for pyroc hlores by Vandenborre et
86 al. 93 and applied to perform a detailed comparison across a series of titanate and stannate pyrochlores. Based on this Raman and IR spectroscopy techniques are used to gain insight into the nature and characteristics of the local struc ture of Bi 2 Ti 2 O 7 and corroborate the crystallographic and computational studies performed in Chapter 4 on the crystal structure of Bi 2 Ti 2 O 7 in particular as it relates to its non correlated atomic displacements 94 6.2 Raman Spe ctroscopy As discussed at length by Esquivel Elizondo et al. 26 Bi 2 Ti 2 O 7 can be consid ered a metastable compound, with dissociation into Bi 4 Ti 3 O 12 and Bi 2 Ti 4 O 11 commonly occurring. This crystal chemistry had previously prevented the synthesis of Bi 2 Ti 2 O 7 sintered ceramics until fast firing technique like microwave sintering were used. Bec ause Raman spectroscopy provides the capability to measure the spectra of samples that are sintered solids, powders, or even particulates suspended in a fluid, it is an excellent tool for characterizing whether a material undergoes a structural transformat ion when sintered or processed. Therefore, spectra of Bi 2 Ti 2 O 7 were taken in both powder and solid pellet form. These spectra, shown in F igure 6 1 were identical for the powder and pellet samples, further confirming that sintering of Bi 2 Ti 2 O 7 powder doe s not induce a structural change, in agreement with X ray diffraction results. 26 This lends further evidence in favor of the modified phase diagram, 26 which establishes the appearance of the pyrochlore phase in the Bi 2 O 3 TiO 2 system.
87 Figure 6 1. Room temperature Raman spectra of Bi 2 Ti 2 O 7 powder and sintered pellet. The Bi 2 Ti 2 O 7 Raman spectrum was analyzed by solving for the imaginary part of the Raman susceptibility in order to observe and fit the individual vibrational modes. This was accomplished through the transformation of the measured data to find the imaginary part of the Raman susceptibility, 95 The susceptibility is a function of the Raman scattering cross section and the Bose scattering factor. This was resolved by treating the collected data with the Bose Einstein distribution, n ( ). (6 3) The transformed Raman susceptibility was modeled using a sum of Lorentzian functions used to assign the Raman modes, as shown in F igure 5 2 (6 4)
88 where each fitted peak is characterized by a center frequency o a local maximum A j and a width j Figure 6 2. Raman spectra transformed by the Bose Einstein factor. The obtained imaginary part of the Raman susceptibility was fitted to a sum of Lorentzian functions The f igure shows the data (black), the fit (red), and the individual contributions to the fit (blue). This functional form is attributed to samples with homogenous broadening, where the width of the Raman band is related to the damping coefficient j The other functional form is that of Gaussians: (6 5)
89 where I o oj and j are the height, center frequency, and the statistical width of each band, and C is a constant. The Gaussian functional form is used for inhomogeneous broadening where the width of each band is due to a statistical distribution of the resonant frequency oj The results of the Ga ussian fit are shown in Figure 6 3 Figure 6 3. Raman spectra transformed by the Bose Einstein fa ctor. The obtained imaginary part of the Raman susceptibility was fitted to a sum of Gaussian functions. The figure shows the data (black), the fit (red), and the individual contributions to the fit (blue). Table 6 2 shows parameters obtained from th e Lorentzian fitting. The Bi 2 Ti 2 O 7 modes were assigned by comparing to typical bismuth and titanate pyrochlores 95 97 as shown in Table 6 2, but with the addition o f normally infrared active F 1 u Because the area of each fitted mode is an arbitrary value (hence the representation by integrated
90 intensity), the error presented is the calculated standard error of each mode l area. Table 6 2. Parameters for Bi 2 Ti 2 O 7 in the Lorentzian fitting of the Raman spectra. Integrated intensity (arb. u.) oj (cm 1 ) j (cm 1 ) Assignment Type Error 13 85 41 F 1u O A O bend & O A 2% 3 146 62 F 1u 15% 100 244 197 F 2g Bi O stretch & O Bi 6% 15 293 83 E g Ti O stretch 20% 14 347 92 E g 2% 43 418 185 F 2g 17% 23 563 114 A 1g O Ti O bend 3% 1 697 55 F 2g Ti O stretch 8% 21 771 163 F 2g 17% Through the automated Lorentzian fit algorithm, nine optically active Raman vibrational modes were identified. These nine peaks each represent an interaction (bend, stretch, breathing, etc.) within the local bonding environment between oxygen atoms and Bi or Ti atoms. The Raman mode properties are a function of the force field photon. While each peak is assigned to a main ph oton mode and motion in F igure 6 2 and T able 6 2 it is also true that that when one bond is set into vibration, this motion has an effect on the rest of the lattice; i.e. when a bending occurs between one bond species, the other atomic bonds in the struct ure will bend and stretch in reaction. This combined set of phonon motions have been clearly shown for the pyrochlore structure, by Vandenborre et al. It has been observed that palatinates and stannates display sharp peaks in the spectra, much more than th e zirconates, hafnates and titanates. This difference is explained by a greater deviation from ideal pyrochlore symmetry ( D 3d ) in the latter compounds. 91 As such, materials with high degree of non correlated atomic
91 displacements will typically exhibit broad peaks within the Raman spectra. Therefore, here we propose that the relatively broadening of the Raman peaks observed is the result of the atomic position displacement causing local asymmetry within the crystal that produces a stronger force field reaction from a single phonon interaction. In previous studies of pyrochlore titanates 18 valence force field constants for stretch, bend, and combination bend stretch interactions have been calculated for a variety of compounds. The potential energy of each mode is dependent on the sum of the strength of each contributing interaction, namely how the strength of the valence force and the inco ming photon cause a series of singular or multiple elastic interaction throughout the lattice. Low frequency Raman modes found in pyrochlores are generally found to be a combination of several bends and stretches, as photon interactions on the lattice due to single bends/stretches induce elastic effects at other sites. Calculation of individual interaction valence force fields in Bi 2 Ti 2 O 7 is beyond the scope of this work; however, based on the trends observed in other pyrochlores, we postulate that modes fi tted to large and wide Lorentzian indicate that the interaction causing the vibration arises from a combination of several motions, each contributing an additional amount of energy into the vibration. For example, the F 2g mode centered at 244 cm 1 has a w idth of 197 cm 1 which is attributed to the combination of the Bi O stretch and the O Bi bend motions. Likewise, sharper peaks indicate that a vibrational mode is primarily influenced by a single interaction. It is important to note that previous work on the theoretical Bi 2 Ti 2 O 7 structure and vibrational spectra was performed by Patterson through DFT. 98 The DFT calculations performed by Patterson were performed for Bi 2 Ti 2 O 7 in both the Pna2 1 and crystal
92 structures. However, both structural studies and the data presented in this paper confirm that Bi 2 Ti 2 O 7 has a cubic structure. Although the Bi ion displacement was included in these DFT calculation s, the theoretical Raman spectra did not predict the Raman active F 1u modes observed in this work. To reconcile this, it is worth mentioning that in general, pyrochlores have their A O atom interactions dominant at low frequencies and their B O atom inte ractions prevalent and at high frequencies. The low frequency range of the Raman spectrum (from 70 180 cm 1 ) has been proposed to be composed of typically IR active F 1u vibrational modes due to the non correlated atomic displacements of the A site observe d in Bi pyrochlores. 95 In a study of Sm, Gd, Yb, and Y titanate pyrochlores by Vandenborre 18 Raman spectra comparison of low frequency modes were determined to not be fundamental frequencies, and were at tributed to TiO 6 octahedra distortion and/or displacement in the A site cation. The F 1u modes activated primarily due to the O A O and O A 1 similarly occur in the Raman spectra of Bi 2 Ti 2 O 7 due to the displacement of the Bi atom from a high symmetry position in the crystal lattice. 95 As stated before, the Bi atom in Bi 2 Ti 2 O 7 differs from the ideal pyrochlore structure by occupying the 96 g Wyckoff position instead of the 16 c This non correlated atomic displacements in Bi 2 Ti 2 O 7 further supports the idea proposed by Arenas et al. 95 of a relaxation in the selection rules allowing for the F 1u mode to be seen in the Raman spectra. Following this, the 180 500 cm 1 bands are composed of F 2g and E g modes. 95 The first F 2g mode is generally assigned between 200 240 cm 1 for titanates, 96 and in
93 the case of Bi 2 Ti 2 O 7 the lowest F 2g is assigned to the mode observed at 242 cm 1 This vibrational mode is attributed to a combination of a stretching interaction between the Bi O bonds, which induc es an additional bending in the O Bi E g modes assigned to 294 and 347 cm 1 and the F 2g mode assigned at 419 cm 1 are mainly due to a stretching of the Ti O bond which cause a reaction from other O Ti O bonds. The higher frequencies consist of A 1g and F 2g vibrational modes, which are purely due to the Ti O modes. 97 The lower A 1g mode, assigned at 564 cm 1 is due to O Ti O bond bending. The two highest modes are designated as F 2g and are assigned at 697 and 771 cm 1 and are entirely due to the stre tching of the Ti O bond. Table 6 3 presents t he vibrational modes of several pyrochlore titanates with their corresponding frequencies. The Bi 2 Ti 2 O 7 Raman modes follow the general behavior of the titanate pyrochlores up until the 500 cm 1 range, at which point the A 1g and F 2g modes are observed at notably higher frequencies, in disagreement with the theoretically calculated modes. 98 This can be explained by a possi ble disorder in the titanium position in the Bi 2 Ti 2 O 7 crystal structure, which would affect the Ti O bond interactions, Table 6 3. The observed Raman vibrational mode frequencies of bismuth and titanate pyrochlores F 2g / E g F 2g A 1g F 2g F 2g Y 2 Ti 2 O 7 93 225 -318 333 -527 531 586 Gd 2 Ti 2 O 7 99 205 260 310 325 450 517 554 677 Dy 2 Ti 2 O 7 99 212 269 308 328 451 519 550 693 Ho 2 Ti 2 O 7 99 214 297 311 329 452 522 562 701 Lu 2 Ti 2 O 7 100 188 -313 336 458 520 609 712 Experimental Bi 2 Ti 2 O 7 -244 293 347 418 563 697 771 Theoretical Bi 2 Ti 2 O 7 98 -262 281 -395 535 537 711 Bi 3/2 MgNb 3/2 O 7 95 -230 346 -419 511 599 786 Bi 3/2 MgNb 3/2 O 7 95 -216 297 -430 529 620 758 Bi 3/2 Zn 0.92 Nb 3/2 O 6.92 95 -256 342 -420 526 610 766 Bi 3/2 ZnTa 3/2 O 7 95 -208 281 -434 540 624 744
94 and accordingly the A 1g and F 2g modes. Recalling the large isotropic parameter assigned to the Ti atom, the observed Raman spectra prov ide additional evidence suggesting that the Ti atom may in fact be locally displaced, 26 which would in turn affect Raman interactions. 6.3 Infrared Sp ectroscopy 6.3.1 Reflectance s pectra The temperature dependent reflectance of a sintered Bi 2 Ti 2 O 7 pellet over 30 and 37000 cm 1 is shown F igure 6 4 The high reflectance value seen at low frequencies is consistent with the large static permittivity value s of Bi 2 Ti 2 O 7 As temperature changes, the spectra change only slightly, with a few percent increase at lower temperatures. We conclude that there is no phase transition present in this temperature range. Figure 6 4 The reflectance of Bi 2 Ti 2 O 7 at tem peratures between 20 and 300 K
9 5 6.2.2 Kramers Kronig analysis The frequency dependent phase shift upon reflection can be calculated from the measured single bounce reflectivity via the Kramers Kronig integral. 101 The high frequency behavior of Bi 2 Ti 2 O 7 from 80,000 to 242,000,000 cm 1 (10 30 ,000 eV) is determined using scattering functions from Henke, 102 and is based on the density and cubic structure of the pyrochlore. The behavior above this range is taken to follow free 4 The gap between the 37,000 cm 1 end to the measured reflectance and the start of the calculated X ray data is bridged with a power law to the 1 uses the reflectance calculated from the oscillator model fit described in the next section. With the phase shift calculate d from measured data using Kramers Kronig methods, other optical constants, including the real and imaginary parts of the dielectric constant ( F igures 6 5 and 6 6) and the optical conductivity ( F igure 6 7 ), can be easily found. 101 We note that the optical conductivity and permittivity plot s show the widths of the phonons to be quite substantial. This, however, is not in disagreement with Chen et al. who also found broad phonon spectra in Bismuth based pyrochlores. 92 We can also see from the real part of the p ermittivity, that there is a weakening of the mode at 160 cm 1 with decreasing temperature. There is a corresponding softening of this peak in Figures 6 6 and 6 7 The interband electronic contribution to the optical conductivity can b e clearly seen in the inset of F igure 6 6
96 Figure 6 5 2 Ti 2 O 7 at temperatures between 20 and 300K Figure 6 6 2 Ti 2 O 7 at temperatures between 20 and 300 K.
97 Figu re 6 7 The real part of the optical conductivity ( 2 Ti 2 O 7 at temperatures between 20 and 300 K. 6.2.3 Oscillator model a nalysis To complement the Kramers Kronig analysis and in order to assign the contribution to the permittivity from each mode, oscillator model fits were conducted on the measured reflectance. Oscillator fits of the experimental measurements are obtained by the dispersion analysis (DA) method, which solves for each oscillator based on its strength, width, and frequency. The DA met be in agreement with the oscillators. To solve for the reflectance the Fresnel formula is employed. (6 4 )
98 with R ( ) the reflectance, n the refractive index, and k the extinction coefficient of the material. In turn, n and k are related to the dielectric function via : (6 5 ) the real and imaginary parts of the dielectric function given as: (6 6 ) (6 7 ) Each oscillator is described by its strength j width j and frequency j As previously discussed, a factor group analysis that uses the displaced coordinates (albeit without Ti displacement, as shown in T able 6 1 ) yields a total of 12 allowable IR active modes. Here, 13 oscillators are required to fit the infrared reflectivity spectra for Bi 2 Ti 2 O 7 The parameters for these oscillators are presented in Table 6 4 The longitudinal optic (LO) modes occur at the zeroes of the undamped dielectric fu nction. We estimate the LO mode frequencies here by temporarily setting the damping of the fit to 0.1 cm 1 and observing the zero crossings of the real part of the permittivity. mode below 30 cm 1 Without this mode, the static dielectric constant, obtained by summing the lattice and electronic contributions from the fit, is ~ 85, lower than the diel ectric constant shown in Chapter 5 sum = 115. The additional low frequency mode may account for this difference.
99 Table 6 4. Parameters for the phonon modes in the 20 K infrared spectrum of Bi 2 Ti 2 O 7 An asterisk (*) indicates mode splitting. A double asterisk (**) indicates a split A ) indicates modes that are observed but not included in the fit as described in present work. Bi 2 Ti 2 O 7 20 K Mode Mode assignment Resonant frequency 1 ) Oscillator Damping coeffic ient 1 ) LO Mode 1 ) 7 A Bend ~10 ---7 A Bend 39 20.6 27 44 7* A Bend 56 4.70 24 59 7 A Bend 77 4.81 35 80 6 (O A O) Bend 186 42.9 68 265 5 (A BO 6 ) Stretch 273 1.40 77 319 4 (O B O) Bend 3 57 3.05 58 386 4 (O B O) Bend 398 1.36 57 474 3 (A O) Stretch 483 0. 365 41 528 2 (A Stretch 532 0.103 43 566 1* (B O) Stretch* 569 0.0653 38 612 1* (B O) Stretch 613 0.0123 18 647 1 (A Stretch 650 0.0147 12 700 n ** 764 0.0301 35 77 4 3.05 (Sum) 85.3 Because of the large mass of Bi, the resonance frequencies of low frequency oscillators in conventional pyrochlores are pushed down to even lower frequency
100 values. A comparison of titanate pyrochlores performed by Kumar et al. shows the trend of decreasing low frequency oscillators as the mass of the A site atom increases. 103 Bismuth is the heaviest atom crystallizing a titanate in the pyrochlore structure, and thus A bend and O A O bend m odes are expected to be pushed down to lower frequencies when compared with previously reported pyrochlore titanates. The O A O bend mode is observed at 186 cm 1 and the O A O bending mode is observed at the lower wavenumbers (<77cm 1 ) and through extra polation could possibly be pushed further down near 10 cm 1 which would explain the increase in reflectivity in the low frequency region. Although outside of the scope of this work, it would be ideal to complement this data with terahertz spectroscopy in vestigations to further corroborate this interpretation. Finally, the data show that bismuth titanate exhibits a phonon mode at around 764 cm 1 n ** in T able 6 4 This feature is also observed in BZN and related pyrochlores has been attributed to disorder of A and static displacements of the 92 this A 2 Ti 2 O 7 Taken as a whole, the Raman and IR spectra are strong evidence of non correlated atomic displacements of both the A and B site of Bi 2 Ti 2 O 7 Bismuth non correlated atomi c displacements are shown by the presence of an IR assigned mode in the Raman spectra. The atypical behavior of the Ti O modes in the higher range of the Raman spectra provide evidence of displacement of the Ti atomic position. The IR spectra further rev eals disorder in th n ** mode.
101 6.4 Conclusion The Raman spectra of the pyrochlore Bi 2 Ti 2 O 7 was measured on both calcined powder and sintered ceramic, showing that both spectra were identical. This provides eviden ce that no major structural change occurs during sintering. Raman modes were assigned by comparison to other bismuth and titanate pyrochlores found in literature, Bi 2 Ti 2 O 7 displays evidence of non correlated atomic displacements in both the A and B site. A low frequency F 1u mode (normally IR active) is assigned in the Raman spectra, due to the relaxation of the selection rules resulting from the displacement of the Bi atom from its ideal crystallographic position. Additionally, evidence of displacement i n the Ti atomic position is provided by the atypical spectroscopic behavior of the Ti O modes at the higher range of the Raman spectra. The IR spectra were fit to an oscillator model from which the real and imaginary parts of the dielectric function were obtained. The low frequency O A A n ** also
102 CHAPTER 7 ORIGIN OF DIELECTRIC RELA XATION IN PYROCHLORES 7.1 Introduction In this C hapter, an overview of all pyrochlores exhibiting dielectric relaxation will be performed and, with the synthesis and characterization of Bi 2 Ti 2 O 7 and other pyrochlores synthesized in this dissertation, gain a comprehensive understanding of the necessary conditions required in pyrochlores to display dielectric relaxation. To start with a brief history, the phenomenon dielectric relaxation in bismuth based pyrochlore systems was first reported by Golovshchiko va et al. 104 finding that this dielectric anomaly had two main character istics for relaxation: 1. Dispersive decrease in the dielectric permitt ivity with increasing frequency 2. Cann et al. then performed a detailed investigation on the dielectric properties of s everal compounds confirming the presence of dielectric relaxation in various bismuth pyrochlores. 21 Since then significant progress has been made to further the knowledge of dielectric relaxati on in pyrochlores, including by the Nino research group. Over the last 20 years there has been an explosive growth of interest in the dielectric properties of pyrochlores. It is not surprising perhaps, as bismuth pyrochlores combine a focus on materials wi th very strong practical properties and a challenging fundamental consideration. The focus on understanding relaxation in pyrochlores stemmed from the synthesis and characterization of Bi 1.5 Zn 1.0 Nb 1.5 O 7 (BZN), which has become the archetypal material for p yrochlore relaxation behavior. 13 105 The dielectric relaxation phenomenon was introduced in Chapter 2, where the te an understanding of relaxation in pyrochlores relevant experimental and theoretical
103 facts observed in the areas of investigation covered in this thesis, as well as results reported in literature, are summarized below: 1. T m follows an Arrhenius behavior. This allows for the calculation of attempt jump o ). In BZN this corresponds to the bending phonon mode assigned to the A site. 45 2. Calculated activation energies range between 0.112 0.559 eV 21 23 4 5 72 87 88 These values are similar to those found in similar relaxing systems such as relaxor ferroelectr ics and dipolar glasses. 3. The A cations in displaced pyrochlores are randomly displaced (along six <0 > equivalent directions) from the ideal pyrochlore positions. In addit are randomly displaced among six directions. These displacements are seen in BZN which also has similar displacements as well as chemical substitutions in both the A and B sites. 4. There have also been studies confirming the existence of sh ort range of displacement for the A site cation in BZN. 106 This A site random occ upancy breaks up the translational symmetry of the lattice. 5. Vibrational spectroscopy of BZN determined that up to ~80% of the dielectric A A O bond bending phonon modes. Based on the phonon modes, activation energy, a nd attempt jump frequency it has been suggested that the dielectric relaxation may be due to local atomic hopping events of the A site cations in the A 2 network. 1 In the remainder of this C hapter, a formalism on the necessary and sufficient conditions for the appearance of dielectric relaxation in pyrochlores will be discussed using the additional knowledge gained from the new pyrochlores systems studied in thi s dissertation 7.2 Discussion Table 7 1 shows a summary of the pyrochlores reported in literature that display dielectric relaxation and which of the three conditions for relaxation are present in each material. Cation substitution was further broken down to A site only, B site only, or both A and B site substitution.
104 Table 7 1. Pyrochlores and the conditions present for possible relaxation Material Polarizable Lone Pair A site A and B site substitution A site substitution B site substitution Atomic Di splacements Relaxation Key Reference Bi 2 ( ScNb ) O 7 Yes -No Yes Yes Yes 21 Bi 2 ( ScTa )O 7 Yes -No Yes Yes Yes 21 (Bi 1.5 Zn 0.5 )(Z n 0.5 Nb 1.5 )O 7 Yes Yes --Yes Yes 13 (Bi 1.5 Zn 1.5 )(Zn 0.5 Ta 1.5 )O 7 Yes Yes --Yes Yes 25 Bi 1.657 Fe 1.092 Nb 1.150 O 7 Yes Yes --Yes Yes 24 Bi 1.67 Mg 0.64 Nb 1.53 O 7 Yes Yes --Yes Yes 47 Bi 1.68 Ni 0.747 Nb 1.493 O 7 Yes Yes --Yes Yes 47 Bi 1.657 (Fe 0.983 Al 0.109 )Nb 1.150 O 7 Yes Yes --Yes Yes 48 Bi 2 (InNb)O 7 Yes -No Yes Yes Yes 23 (Bi 1.93 Fe 0.07 )(F e 1.42 Te 0.58 )O 7 Yes Yes --Yes Yes 49 Ca 1.46 Ti 1.38 Nb 1.11 O 7 No Yes --Yes Yes 50 Since most of the research work has focused on Bi pyrochlores, and especially BZN, a review of the phenomenon showed that in all cases investigated relaxation occur s when: 1. A polarizable lone pair cation occupies the A site 2. There is cation substitution 3. Atomic displacement is present In order to isolate the effects of having a highly polarizable A site on dielectric relaxation in pyrochlores Roth et al. synthesized a displaced and substituted pyrochlore without a lone pair containing cation in the A site, Ca 1.5 Ti 1.5 NbO 7 (CTN) 50 While this pyrochlore does not contain a highly p olarizable A site, it still has the displacive disorder in the A 2 network and chemical substitution in both the A and B site similar to the other pyrochlores that exhibit relaxation, such as BZN. CTN does in fact display dielectric relaxation behavior, this behavior suggests that the presence of polarizable lone p air cations (such as Bi 3+ ) is not necessary in order for pyrochlores to display dielectric relaxation.
105 The work in this dissertation has focused on Bi 2 Ti 2 O 7 due to the fact that it is the only stoichiometric bismuth based cubic pyrochlore which also exhibi ts atomic displacement. Bismuth titanate presents an opportunity to isolate the effect of atomic displacements without cation substitutions on dielectric relaxation. In an effort to isolate the effects of cation substitution without atomic displacements s everal different pyrochlores were synthesized. In particular, the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 pyrochlore present a unique opportunity to isolate A and B site substitution without atomic displacements. Table 7 2. New pyrochlores from this work a nd the conditions present for possible relaxation Material Polarizable Lone Pair A site A and B site substitution A site substitution B site substitution Atomic Displacements Relaxation Reference Bi 2 ( ScNb ) O 7 Yes -No Yes Yes Yes 21 Bi 2 ( ScTa )O 7 Yes -No Yes Yes Yes 21 (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 Yes Yes --Yes Yes 13 (Bi 1.5 Zn 1.5 )(Zn 0.5 Ta 1.5 )O 7 Yes Yes --Yes Yes 25 Bi 1.657 Fe 1.092 Nb 1.150 O 7 Yes Yes --Yes Yes 24 Bi 1.67 Mg 0.64 Nb 1.53 O 7 Yes Yes --Yes Yes 47 Bi 1.68 Ni 0.747 Nb 1.493 O 7 Yes Yes --Yes Yes 47 Bi 1.657 (Fe 0.983 Al 0.109 )Nb 1.150 O 7 Yes Yes --Yes Yes 48 Bi 2 (InNb)O 7 Yes -No Yes Yes Yes 23 (Bi 1.93 Fe 0.07 )(Fe 1.42 Te 0.58 )O 7 Yes Yes --Yes Yes 49 Ca 1.46 Ti 1.38 Nb 1.11 O 7 No Yes --Yes Yes 50 Bi 2 Ti 2 O 7 Yes No No No Yes No This Work Sm 2 Ti 2 O 7 No No No No No No This Work (Sm 0.25 Yb 0.75 ) 2 Ti 2 O 7 This Work (Sm 0.5 Yb 0.5 ) 2 Ti 2 O 7 No -Yes No No No This Work (Sm 0.75 Yb 0.25 ) 2 Ti 2 O 7 This Work Sm 2 (Sn 0.5 Ti 0.5 ) 2 O 7 No -No Yes No No This Work With the addition of these new pyrochlores to Table 7 2 one can provide key insights into what requirements are necessary in order to display dielectric relaxation.
106 As stated before, the observation of dielectric relaxation in the Ca Ti (Nb,Ta) O pyrochlores 50 discards the presence of lone pair electrons or highly polarizable lone pair cations as a necessary condition for the emergence of dielectric relaxation in pyrochlores. Nevertheless, atomic displacements and substitutional cations are present in those Ca pyrochlores. The dielectric and structural analysis of Bi 2 Ti 2 O 7 in this work has revealed that combined atomic displacements and high polarizability of the A site are no t enough to lead to the onset of dielectric relaxation. This result in combination with the observations in Ca pyrochlores suggests that substitutional cations play an essential role in the emergence of relaxation behavior in these compounds. The synthesi s and characterization of the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 pyrochlores allowed for the study of the effects of chemical substitution. Both systems are ideal pyrochlores and do not show evidence of displacements. As shown in C hapter 5 these pyrochl ores do not display dielectric relaxation. W hile chemical substitutions are a necessary condition for dielectric relaxation it is not sufficient to induce dielectric relaxation without the presence of atomic displacements. It is clear that the combinati on of substitutional cations and atomic displacements play a key role in dielectric relaxation. In order to understand the impact of these two factors a further look into the dynamics of the local environment and electronic structure of BZN and Bi 2 Ti 2 O 7 is necessary. The effect of substitutional cations in BZN on the local structure was investigated by Withers et al. using electron diffraction and Monte Carlo calculations Guidelines for the preferred orientations of Zn cations in the A 2 2 O 6 sub networks were proposed. These guidelines can be briefly summarized as randomly distributed Zn B in
107 the B 2 O 6 network and <211> directional ordering of Zn A cations with one Zn A per A 2 O tetrahedron. Building off these proposed guidelines, DFT calculations performed by Hinojosa et al. allowed for the visualization of the energy landscape of the A site cation in BZN and Bi 2 Ti 2 O 7 Figure 7 1 presents the electronic localization function (ELF) for a portion of the ( 11) plane for the Bi 2 Ti 2 O 7 and BZN systems. An outline (dashed 4 tetrahedra sub network and the A site displacement directions are also highlighted (black arrows for in plane and white circles for out of plane displacements). I n Figure 6 2, the Bi lone pairs are asym metric and point away from the cation and in the opposite direction of the atomic displacement in both BZN and Bi 2 Ti 2 O 7 preferentially displace towards the Zn A cations. The n ature of the correlated atomic displacements in Bi 2 Ti 2 O 7 can be understood by comparing the ELF of Bi 2 Ti 2 O 7 and BZN. Without the presence of another cation on the A site, the correlated displacement provides an even distribution of the lone pair electrons onto the BO 6 octahedra network reducing the stereochemical strain associated with the presence of the lone pair electrons. 26 107 109 In BZN, however, the Zn A cations reduce the interaction between the A 2 2 O 6 sub networks and open up the confined space allowing for the incorporation of the Bi lone pairs. Therefore by having substitutional cation s, BZN breaks the correlated displacement arrangement of the Bi cation displayed by Bi 2 Ti 2 O 7
108 A B Figure 7 1. The electron localization function (ELF) for a portion of the ( 11) plane for A) Bi 2 Ti 2 O 7 and B) BZN pyrochlore compounds from 0.0 ( delocalized) in blue to 1.0 (fully localized) in red. The cation displacements are indicated by the solid black arrows (in plane displacement) or the white circles (out of plane displacement). Figures adapted from Hinojosa et al. 108 In addition to affecting the ELF, it is clear that the inclusion of cation substitutions significantly affect the energy profiles and cation pathways for hopping between crystallogr aphic positions. Further calculations were undertaken by Hinojosa et al. to map the relative energy landscape of BZN and Bi 2 Ti 2 O 7 allowing for the visualization the atomic hopping among the 6 possible equivalent A site positions.
109 A B Figure 7 2. Th e relative energy landscape from 0.0 (blue) to 1.0 eV (red) plotted with respect to the x and y position for one Bi cation in A) Bi 2 Ti 2 O 7 and B) BZN. Figure adapted from Hinojosa et al. 108 The relative energy landscape of Bi 2 Ti 2 O 7 and BZN are shown in Figure 6 2. Through this type of plot it is easy to see that the Bi cations prefer to hop along the
110 periphery of the 96 g ring in Bi 2 Ti 2 O 7 It is also evident that once Bi hops out of the lower energy states (s1, s2, and s3), the hopping events cost considerably more energy. However, unlike B i 2 Ti 2 O 7 the Bi cations in BZN do not follow the 96 g ring to jump between equivalent positions but instead the Bi cation s trans ition through the center of the 96 g ring This type of jumping results in nearly the same energy costs for a single site hop or double or even a triple site hop Therefore, in BZN the Bi cations readily respond to an applied electric field and may undergo any type of hopping event even flipping across the 96 g ring with approximately the same activation energy. In contrast, the Bi cations in B i 2 Ti 2 O 7 are limited in the types of hops (since they move along the outside of the 96 g ring) they may undergo due t o the local bonding environment and often these jumps cost considerably more energy. The ELF and energy landscape visualizations help visualize why there needs to be both atomic displacements and substitution in order for dielectric relaxation in pyrochl ores to take place. This is further confirmed by the absence of relaxation in both the Sm systems and Bi 2 Ti 2 O 7 presented in C hapter 6 7.3 Conclusion T he work presented in this dissertation adds a link to the conditions required in pyrochlores to exhibit d ielectric relaxation An in depth investigation into the structure and dielectric properties of Bi 2 Ti 2 O 7 showed that a pyrochlore displaying atomic displacements without substitution does not induce relaxation. This result points suggests that substitution al cations play a major role in the origin of dielectric relaxation in pyrochlores.
111 By investigating the dielectric response of the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 pyrochlore systems the impact of cation substitutions on relaxation was targeted; as b oth systems are ideal pyrochlores and do not show evidence of displacements. As shown in Chapter 5 these pyrochlores do not display dielectric relaxation. W hile chemical substitutions are a necessary condition for dielectric relaxation it is not sufficien t on its own to induce dielectric relaxation without the presence of atomic displacements. Therefore, in order to display dielectric relaxation in pyrochlores it is necessary to have both atomic displacements and cation substitutions. The presence of ju st one of these factors is not enough to induce relaxation. The DFT calculations of Bi 2 Ti 2 O 7 show that the Bi cation displays correlated displacements. However, by incorporating cation substitution into BZN this correlation is broken giving the Bi cation t he freedom to hop to any possible site. On the other hand, Bi 2 Ti 2 O 7 shows a higher energy cost and is limited in the type and number of possible cation hops. A break in the local symmetry of the material (impeding the coordinated displacements) may be the ultimate answer to the origin of relaxation, where random displacements are necessary in order to accommodate the ca tion hopping of the A site cation through the center of the 96 g ring
112 CHAPTER 8 DIELECTRIC PROPERTIES OF TYPE II Bi 3 NbO 7 8.1 Introduction It is well known that the high Bi 2 O 3 form is stable between 729C Bi 2 O 3 phase can be described as an oxygen deficient fluorite structure, also known as defect Bi 2 O 3 exhibits a number o f unique features, there is significant interest in stabilizing this phase below 729C transition temperature. Examples of the these unique crystallochemical characteristics include a high polarizability of the cation network, the ability of bismuth cati ons to dynamically accommodate asymmetric surroundings 110 and the anion network contains 25% intrinsic oxygen vacancies due to the stoichiometry of the unit cell 111 Typically, in order to maintain these desirable properties a phase stabilization using Bi substitution with different metal cations is performed 112 114 Among the vast Bi 2 O 3 structure, the (Bi 2 O 3 ) 1 x (Nb 2 O 3 ) x BN SS ) system is widely used due to the fact that these materials exhibit very high oxygen ion conductivity in combination with electr onic conductivity 115 116 BN SS have revealed four main superstructures (types I IV). At 25 mol% Nb 2 O 5 two crystal structures have been reported: type I at the Bi rich end was found to be a sillenite related phase of composition Bi 12 Nb 0.29 O 18.7+x 117 and is not related to the fluorite Bi 2 O 3 118 Type II Bi 3 NbO 7 a cubic defect fluorite structure 119 type III Bi 3 NbO 7 an ordered tetragonal fluorite type superstructure 118 and type BN SS (Bi 5 Nb 3 O 15 ) adopts an Aurivillius related phase 120 There has also been
113 investigation of the microwave dielectric properties of the Bi 2 O 3 Nb 2 O 3 system due to its possible compatibility with low temperature cofired ceramic (LTCC) technology 121 Recently, single crystal type II Bi 3 NbO 7 has been synthesized via floating zone crystal growth by Ling et al. 122 In this work an investigation into the dielectric properties of type II Bi 3 NbO 7 single crystal as a function of temperature and frequency allows for correlations in the structure diel ectric properties within fluorite related structures. 8.2 Dielectric Spectroscopy Figure 8 1 shows the dielectric properties of type II Bi 3 NbO 7 as a function of temperature at different frequencies from 1 kHz to 2 MHz. The real part of the permittivity decreases from 87 to 81 between 300 and 20 K. The real part shows two slope variations with associated changes in the imaginary part with a peculiar cross over at approximately 100 K, followed by a slight increase in loss around 40 K. Dielectric relaxati on is a phenomenon observed in many bismuth pyrochlores 12 22 23 45 70 71 where these materials exhibit a step like decrease in the real part of the dielectric permittivi ty accompanied by a frequency dependent peak in the imaginary part. However, the imaginary peaks present in type II Bi 3 NbO 7 are very diffuse, and the behavior of Bi 3 NbO 7 does not provide a clear evidence of a dipolar relaxation event. At higher temperatu res (approx. 400 K) frequency dispersion in the real part of the relative permittivity occurs, accompanied by a sharp increase in the imaginary part at 1 kHz (~9 at 400 K). This behavior is consistent with the onset of electrical conduction.
114 Figu re 8 1. Real and imaginary part of the permittivity of single crystal type II Bi 3 NbO 7 at 1 kHz, 10 kHz, 100 kHz, 500 kHz, 1 MHz, 1.2 MHz, 1.5 MHz and 2MHz. To further analyze the dielectric response of type II Bi 3 NbO 7 one can characterize the onset of el ectrical conduction by viewing the imaginary components of the dielectric functions (i.e. impedance ( Z ), admittance ( Y ), permittivity ( ), and modulus ( M )). This analysis also allows for the investigation of whether dielectric relaxation occurring along with conductivity. As shown in the work by Cao and Gerhardt 85 conductivity will result in M Z function. Therefore, both the and the peaks will overlap throughout the entire frequency range, thereby giving a clear indication that conductivity is occurring. It
115 F ig ure 6 2 was observed that Bi 3 NbO 7 begins to display this behavior at 473 K. In the A B Figure 8 2. Normalized functions of the imaginary components of the im pedance ( ), admittance ( ), modulus ( ), and permittivity ( ) at A ) 473 K and B ) 150 K
116 By analyzing the dielectric functions as a function of frequency in F igure 8 2 A it is clearly evident that and display clear peaks over the same frequ ency range while both the and have no observable peak in this frequency range, showing that the onset of conduction begins at 473 K and there is no observable dielectric relaxation occurring due to the fact that there is no observable over the measured frequency range. Figure 8 2 B shows the dielectric functions as a function of temperature at 150 K. It is important to note that, unlike F igure 8 2 A the does not have an observable peak in this frequency range, ruling out conduction. Furthe r, since the does not have an observable peak in this range, it can be inferred that no clear dielectric relaxation is occurring at 150 K over the observed frequency range. It is worth noticing that the dielectric behavior displayed by type II Bi 3 N bO 7 is very similar to that displayed by Ln 3 NbO 7 (Ln = Dy, Er, Yb and Y), rare earth niobates that also adopt a defect fluorite structure 113 8.3 Defect Fluorite Structure Dielectric Property Relationship To recall briefly, Weberite type Ln 3 BO 7 compounds (where Ln 3+ is a rare earth element, and B is Os 5+ Re 5+ Ru 5+ Re 5+ Mo 5+ Ir 5+ Sb 5+ Nb 5+ or Ta 5+ ) have attracted attention d ue to their interesting magnetic 123 125 dielectric 126 127 and photocatalytic properties 128 129 Weberites and pyrochlores, expressed as A 2 B 2 O 7 can be seen as anion deficient superstructure derivatives of the fluorite structure (MO 2 ). A review on weberites was recently published by L. Cai and coworkers 130 The series Ln 3 NbO 7 (Ln = Nd, Gd, Dy, Er, Yb, and Y) has been previously investigated and a change in the crystal structure from defect cubic fluorite to orthorhombic weberite type structures with increasing Ln 3+ ionic radius was reported 127
117 Specifically, the cubic defect fluorite structure in Ln 3 NbO 7 was shown to be stabilized when the ionic radius of the rare earth is equal or less than that of Dy 3+ (1.20 7 ) 131 Unlike pyrochlores (A 2 B 2 O 7 ) in which A, B and the oxygen vacant sites have ordered arrangements, the defect fluorite structure has both disordered cations as well as disordered oxygen deficiency sites. The real part of the permittivity of the Ln 3 NbO 7 follow the same trend although the permittivity of type II Bi 3 NbO 7 is significantly higher. The imaginary component of the permittivity is also very similar to that of that of Ln 3 NbO 7 although type II Bi 3 NbO 7 has higher losses and the onset of conduction occurs at significantly lower temperatures. For compa rison, the lattice parameters of Bi 3 NbO 7 and Ln 3 NbO 7 (Ln = Dy, Er, Yb and Y) are presented in T able 8 1 The parameters were calculated using the Nelson Riley function for cubic structures and through neutron refinement for Bi 3 NbO 7 122 The structure of type II Bi 3 NbO 7 single crystal has been reported by Ling et al. th rough neutron diffraction as a cubic defect fluorite structure with a lattice parameter of 5.479 . Table 8 1. Lattice parameters of Ln 3 NbO 7 (Ln = Dy, Er, Yb, Y) and Bi 3 NbO 7 Compound a () Ionic radius of A site () 132 typeII Bi 3 NbO 7 5.479 1.17 Dy 3 NbO 7 5.2701 1.027 Y 3 NbO 7 5.2534 1.019 Er 3 NbO 7 5.2318 1.004 Yb 3 NbO 7 5.1944 0.985 Astafyev et al. 133 probability of polar distortions of these structures. Using the lattice parameters and ionic radii found in T able 8 1 type II Bi 3 NbO 7 has the largest specific free volume ratio of 50.4% while the other Ln 3 NbO 7 have a ratio between (42 45%). Based on this, it can
118 be reconciled that the openness of the type II Bi 3 NbO 7 structure allows for the reorientation of the dipole s within the structure giving rise to a higher permittivity. This comparative response can be observed in F igure 8 3 where the theoretical permittivity of the structure is calculat ed using the Clausius Mossotti E quation and compared to the experimental p ermitt ivity. The Clausius Mossotti E quation does not factor in dipolar contributions to the permittivity. Therefore, by comparing the theoretical values of permittivity to the experimental, a rough estimate of the dipolar contribution to the permittivity c an be extracted. Figure 8 3. Experimental and theoretical (Clausius Mossotti) permittivity of type II Bi 3 NbO 7 and Ln 3 NbO 7 defect fluorites. For the Ln 3 NbO 7 the difference from the theoretical to experimental permittivity is relatively constant. However for type II Bi 3 NbO 7 this difference is significantly higher
119 and can be attributed to the dipolar component of the permittivity as a result of both of the higher polarizability of Bi and the comparatively openness of the compound. We now turn our attentio n to variation of permittivity as a function of temperature. The temperature coefficient of capacitance (TCC) describes the change in capacitance over a specified temperature range. A review by Harrop et al. 134 presented that materials with higher values of dielectric permittivity (paraelec trics) exhibit extremely negative values of TCC. For capacitive components in electronic applications stability is important and therefore, a flat TCC (e.g. 15 50 ppm/C or MK 1 ) is desirable. This typically achieved by a composite approach mixing two d ielectric compounds with opposite TCC or by compositional tailoring. Cai et al. demonstrated that it was possible to tailor the TCC of Ln 3 NbO 7 (Ln = Dy, Er, Yb, and Y) as a function of ionic radius of the A site 131 Here, the TCC was calculated from 218 to 350 K for Ln 3 NbO 7 (Ln = Dy, Er, Yb, and Y) and compared wi th the value obtained from type II Bi 3 NbO 7 as shown in F igure 8 4 It can be seen that as the atomic radius of the A site increases, the TCC of the defect fluorite Ln 3 NbO 7 decreases and that type II Bi 3 NbO 7 has a positive TCC. However, it is a lower value and seems to follow the general trend of the defect fluorite Ln 3 NbO 7 series, possessing the lowest TCC of the defect fluorite Ln 3 NbO 7 It has been proposed that the TCC in defect fluorite type Ln 3 NbO 7 may increase with structural disorder as the local o rdering should increase with an increasing difference between the ionic radius of Nb 5+ and Ln 3+ 131 Therefore, one would expect the TCC of type II Bi 3 NbO 7 to be significantly lower than any of the defect fluorite Ln 3 NbO 7 as the ionic radius of Bi 3+ is the largest of the series.
120 Figure 8 4. TCC of defect fluor ite Ln 3 NbO 7 and type II Bi 3 NbO 7 from 218 K to 350 K. It is also interesting to note that as the ionic radius of the Ln 3+ increases across the Ln 3 NbO 7 series, there is a change to an orthorhombic weberite related crystal structure when the Ln 3+ > Dy 3+ (1.0 27 ). However, the structure of type II Bi 3 NbO 7 is a defect fluorite despite the fact that the ionic radius of bismuth is larger than the Ln 3+ series. That is, one would expect type II Bi 3 NbO 7 to be orthorhombic rather than a stable defect cubic fluorit e. A possible explanation for this exception may be the fact that bismuth is stereochemically active and highly polarizable 110 which may allow for the accommodati on into a defect fluorite structure. One can further probe into the optimization of the bonding requirements of the cation sites by contrasting bond valence sums (BVS) 135 of the A site in the Ln 3 NbO 7 series with those of type II Bi 3 NbO 7 BVS can be used as a measure of the tendency of the structure to distort. For optimum bonding satisfaction, the BVS for the A site would
121 be equal to its oxidation state i.e., 3 for Bi, in this case. BVS can also show if an atom is under or over coo rdinated. BVS is calculated using E quation 8 1 : (8 1) R o and B are empirical parameters 135 unique to the A site cation. R ij is the bond length from the i site to the j site, in this case A to O. Figure 8 5 shows the BVS for the A site atom in the defect fluorite structure. This structure leads to two possible A O bond lengths (one short, one long), for each of the 7 A O bonds with one oxygen vacancy. The x axis shows the different possible config urations of the structure with the number of longer bonds. For the A site, the most preferable configuration would be one where the BVS is ~3. For most of the Ln 3 NbO 7 series the BVS of ~3 occurs when there are between 2 and 3 longer bonds. However, for t ype II Bi 3 NbO 7, the preferred configuration lies between 4 and 5 longer bonds. For comparison, a theoretical ideal structure of Bi 3 NbO 7 was calculated (with and without an oxygen vacancy) and it can be seen that by adopting a defect fluorite structure typ e II Bi 3 NbO 7 can attain a BVS closer to the ideal value of 3. In addition, the bond strain index can also be used to determine the strain in the bonding arrangements of the structure. It is shown by E quation 8 2 : (8 2) S i j is the experimental bond valence and s ij is the theoretical bond valence of bond ij A structure is typically considered strained when the BSI is greater than 0.05 valence units (vu).
122 Figure 8 5. BVS of Ln 3 NbO 7 and type II Bi 3 NbO 7 defect fluorite s howing the possible bonding arrangements. The dashed and dotted lines represent Bi 3 NbO 7 at the ideal fluorite position for comparison with the defect fluorite Bi 3 NbO 7 structure. Figure 8 6 shows the BSI for the Ln 3 NbO 7 and type II Bi 3 NbO 7 in contrast to the ideal fluorite structure (shown as dotted and dashed line). By adopting the defect fluorite structure, the BSI becomes greater than the 0.2 indicating some strain in the structure. Higher strains are present in the structure with higher number of long bonds. However, F igure 8 5 shows that having around three long bonds the valence of the A site is favored Finally, another useful metric for analyzing the stability of the overall structure is the global instability index (GII), the root square mean of t the expected values for all atoms in the unit cell. (8 3)
123 N is the number of atoms in the unit cell and BVS 0 is the expected BVS. Typical values of stable structure s have a GII < 0.2 vu. I n F igure 8 7 the GIIs of the Ln 3 NbO 7 defect fluorites are shown along with type II Bi 3 NbO 7 in both defect fluorite and ideal fluorite positions for comparison. Figure 8 6. BSI of Ln 3 NbO 7 and type II Bi 3 NbO 7 defect fluorite showing the possible bonding arrangements. The dashed and dotted lines represent Bi 3 NbO 7 at the ideal fluorite position for comparison with the defect fluorite Bi 3 NbO 7 structure. While the Ln 3 NbO 7 follows the same general trend with the GII decreasing as the number of long bonds dec reases, type II Bi 3 NbO 7 does not follow the expected trend shown by the other defect fluorites. In fact, type II Bi 3 NbO 7 displays a minimum GII near three long bonds. This coincides with a BVS of ~4 which is higher than the ideal value of 3. Moving to a mo re favored BVS would lead to a cost in both BSI and GII.
124 Figure 8 7. GII of Ln 3 NbO 7 and type II Bi 3 NbO 7 defect fluorite showing the possible bonding arrangements. The dashed and dotted lines represent Bi 3 NbO 7 at the ideal fluorite position for compari son with the defect fluorite Bi 3 NbO 7 structure. The Nb atom also plays a role in determining the behavior of the GII, which takes a look at the entire bonding environment. Since stabilized in a defect fluorite structure, the Nb atoms are located in the s ame crystallographic position as the Bi atoms, with the main difference being the oxidation state of Nb (+5). The BVS of the Nb atom also shows a similar trend to that shown in F igure 8 5 this is due to the fact that the only difference in the BVS calcula tion is the value empirical parameters R O and B However, unlike the Bi atom, Nb would prefer a BVS of 5 to match the oxidation state of Nb. In the ideal fluorite structure the BVS of the Nb is 3.58 which is much lower than the preferred value of 5. By adopting a defect fluorite structure with 2 long bonds the BVS of the Nb atom increases to 4.23.
125 The GII of the defect fluorite structure of type II Bi 3 NbO 7 shows that the structure is most stable at 2 3 number of long bonds, at this point BVS of the Nb atom is closer to its ideal value than the Bi site. It has been proposed by Castro et al. that type II Bi 3 NbO 7 rearranges its structure in order to both satisfy the coordination of both the Bi and Nb atoms. In this configuration, the Nb atoms are in a cl assical oxygen octahedron and the Bi atoms are in a wide variety of oxygen polyhedra distorted by the stereochemical influence of its lone pair 136 8.4 Conclusion The dielectric properties of type II Bi 3 O 7 single crystal were investigated as a function of frequency and temperature. The dielectric response of type II Bi 3 NbO 7 follows the same behavior as the Ln 3 NbO 7 defect fluorite series, where the real part of the permittivity decreases with decreasing temperature. Due to the fact that bismuth is highly polarizable is displays a permittivity of 85 at room te mperature (1 MHz). The dielectric behavior as a function of frequency was also investigated and the onset of electrical conduction was identified at around 473 K. The TCC of Ln 3 NbO 7 decreases with increasing Ln 3+ ionic radius and type II Bi 3 NbO 7 was fou nd to be 1.53x10 3 ppm/C and followed the same general trend.
126 CHAPTER 9 DIELECTRIC RESPONSE AND PHASE TRANSITION OF Gd 3 NbO 7 9.1 Introduction Weberite type Ln 3 BO 7 compounds (where Ln 3+ is a rare earth element and B is Os 5+ Re 5+ Ru 5+ Re 5+ Mo 5+ Ir 5+ Sb 5+ Nb 5+ or Ta 5+ ) attract great attention because they exhibit interesting properties including magnetic 137 139 dielectric 140 141 as well as phot ocatalytic activity 142 144 Gd 3 NbO 7 belongs to this weberite type family where the BO 6 are corner linked to each ot her and form chains of BO 6 octahedra with parallel chains of LnO 8 distorted cubes. The crystal structure of Gd 3 NbO 7 was first determined by Rossell et al. 145 and assigned a space group of C222 1 at room temperature. Gd 3 NbO 7 undergoes a phase transition at about 340K, which is commonly observed in the Ln 3 BO 7 family 146 148 The existence of a transition has been confirmed through heat capacity measurements 149 and Raman spectroscopy 150 There are conflicting reports on the phase transition that occurs in Gd 3 NbO 7, it has be en suggested that the transition was between Cmm2 to Cmmm without any proof. In a more recent study 75 high resolution X ray diffraction (XRD) was performed, along with heat capacity and second harmonic generation proposed a phase transition from a centrosymmetric space group Cmcm with a transition below 340 K into a non centrosymmetric structure with sp ace group Cm2m However the proposed low temperature phase of Cm2m is a distinct anomaly when compared to other Weberite type Ln 3 NbO 7 where the phase transition goes from Cmcm to C 222 1 137 The difference between the C 222 1 space group and Cm 2 m are nearly identical when looking at XRD data alone. Therefore, in this C hapter the low temperature structure debate of Gd 3 NbO 7 will be resolved by examining its IR behavior,
127 high resolution XRD, and a comparison of the dielectric response of Gd 3 NbO 7 to Gd 3 TaO 7 9.2 Results and Discussion The dielectric behavior of Gd 3 NbO 7 as a function of temperatures at fixed frequencie s from 1 kHz to 1MHz is shown in Figure 9 1. The real part of the permittivity is between 30 and 44 and the imaginary part of permittivity is on the order of 10 4 to 10 1 at 1 MHz from 25 K to 400 K. Figure 9 1. Real and imaginary components of the pe rmittivity of Gd 3 NbO 7 from 500 Hz to 2 MHz It is observed that the dielectric response undergoes a frequency and temperature dependent dielectric relaxation behavior. The real part of the relative permittivity of Gd 3 NbO 7 becomes more dispersive with incr easing temperature, increasing sharply from 25 K to ~ 325 K where a maximum is reached. The temperature at the peaks of the imaginary components occur (T m ) shift to higher temperatures with
128 increasing frequency. This shift in the imaginary component of the permittivity is similar to those observed in Bi pyrochlores, such as BZN, which are undergoing dielectric relaxation. However, unlike the typical Bi pyrochlore relaxation behavior there is no clear shift in the maxima of the real part of the relative perm ittivity. To better understand the phenomena, the Arrhenius function is used to model the relaxation behavior of Gd 3 NbO 7 : (9 1) where v r is the measuring frequency, the pre exponential v o is the attempt jump frequency E a the activation energy and k B T m is determined by fitting the imaginary part of the permittivity for each frequency measured to a Gaussian function. The non symmetric tails of the peaks are cut off during fitting. The resu lting Arrhenius plot is presented in Figure 9 2. From the linear fit, v o = 1.12 x 10 11 Hz, and the activation energy E a is 0.439 eV, which is larger than the typical values observed in Nb based pyrochlores and relaxor ferroelectrics. 151 152 However, other ionic and dipolar compound systems have even higher activation energies; for example, 0.53 eV for CaF 2 do ped NaF and 1.02 eV for (Ba 0.8 Sr 0.2 )(Ti 1 x Zr x )O 3 153 154 Thus, the calculated activation energy is within a n acceptable level.
129 Figure 9 2. Arrhenius plot of temperature at which the maximum loss peak occurs in Gd 3 NbO 7 While very similar to the dielectric relaxa tion discussed in Chapter 5 the lack of dispersion in the real part of the permittivity points to a possible phase transition which has been studied in other similar weberites such as Ln 3 IrO 7 155 Ln 3 MoO 7 156 and Ln 3 RuO 7 157 The specific heat was measured by Cai et al. (Figure 9 3) showed a phase transition between 310 and 340 K. Approaching the structural phase transition, there is a divergence of the specific heat. This transition is consistent with a second order phase transition.
130 Figure 9 2. Heat capacity of Gd 3 NbO 7 Adapted from Cai et al. Infrared spectroscopy as a function of temperature was perf ormed at Professor ~450 cm 1 that disappears above the phase transition temperature (Figure 9 3) Figure 9 3. Infrared Spectroscopy of Gd 3 NbO 7 at 50 K, 300 K, and 360 K. The arrow indicates the mode disappearing above the transition temperature.
131 A comparison of the crystal data and structural refinements of synchrotron XRD is shown in Table 9 1 for the previously proposed low temperature structure Cm 2 m (from Cai et a l. ) and the alternative C 222 1. Table 9 1 Crystal d ata and refinement p arameters of the two proposed low temperature Gd 3 NbO 7 Space Group Cm2m C 222 1 Temperature 295 K 295 K Lattice parameters 7.5324 7.5342 10.6108 10.6185 7.5327 7.5461 Z 4 4 0.414201 0.414201 0.5 ~ 29.999 0.5 ~ 29.999 No. of peaks 404 404 No. of parameters refined 71 65 R wp (%) 10.39 12.14 R p (%) 7.93 9.57 GOF (X 2 ) 5.169 9.104 Both of the refinements for Gd 3 NbO 7 provide a satisfactor y fit, while Cm 2 m has a lower X 2 the refinement needed more fitting parameters than C 222 1 Ideally neutron diffraction would be used to compliment the synchrotron XRD results but Gd poses a significant challenge due to its extremely high neutron absorption Transmission electron microscopy was also used to try to differentiate between the two space groups but the difficulty in identifying a mirror from a two fold rotation proved inconclusive. In an effort to identify the correct low temperature phase of Gd 3 NbO 7 a similar well known Gd weberite was synthesized, Gd 3 TaO 7 The key aspect of this weberite is the fact that it undergoes a transition from Cmcm to C 222 1 15 8 160 The dielectric properties of Gd 3 TaO 7 have not been reported and a comparison of its dielectric
132 response at the phase transition temperature to that of Gd 3 NbO 7 could prove the link to understanding the phase transition of Gd 3 NbO 7 The dielectric be havior of Gd 3 TaO 7 as a function of temperatures at fixed frequencies from 1 kHz to 1MHz is shown in Figure 9 4. The real part of the permittivity is between 25 and 33 and the imaginary part of permittivity is on the order of 10 4 to 10 1 at 1 MHz from 25 K to 300 K. Figure 9 4. Imaginary and real part of the permittivity as a function of temperature from 500 Hz to 2 MHz of Gd 3 TaO 7 Comparing the dielectric response of Gd 3 TaO 7 (Figure 9 4) to that of Gd 3 NbO 7 (Figure 9 1) reveals some interesting differe nces. The permittivity of Gd 3 TaO 7 is ~ 25% lower than to that of Gd 3 NbO 7 which is to be expected as the dipolar polarizability of Nb is about 20 % higher than that of Ta. 161 More importantly, however, is the behavior of the permittivity and loss at the phase transition temperatures. Both Gd 3 TaO 7 and
133 Gd 3 NbO 7 exhibit a sharp decrease in permittivity near the phase transition temperature, however, the major difference is found in the imaginary part of the permittivity. Gd 3 NbO 7 has peaks in the imaginary component of the permittivity, where the maximum increases in temperature with increasing frequency, similar to dielectric relaxation in pyrochlores. On the other hand, Gd 3 TaO 7 does not have any imaginary component anomaly while passing through the transition point from Cmcm to C 222 1 This difference may provide the key for understanding the nature of the dielectric transition in Gd 3 NbO 7 the difference in the dielectric b ehavior of Gd 3 TaO 7 ( Cmcm C 222 1 ) shows no accompanying loss peaks. The loss anomaly in Gd 3 NbO 7 combined with IR, SHG, and XRD data all support a different transition to that seen in Gd 3 TaO 7 the choice of C m 2 m over C 222 1 also generates a net dipole in the structure due to the displacements of the Nb 5+ and Gd 3+ ions along the  75 which is not observed in Gd 3 TaO 7 and may in fact lead to difference in the dielectric response. 9 .3 Conclusion The dielectric behavior of Gd 3 NbO 7 was characterized as a function of temperature, the origin of the dielectric re laxation type behavior is ascribed to the phase transition. The imaginary component of the permittivity was fit to the Arrhenius function and an activation energy of 0.439 eV was obtained. Second harmonic generation (SHG), heat capacity measurements and I R indicated a phase transition in Gd 3 NbO 7 at about 340 K. The lambda shape specific heat capacity near the phase transition suggests a 2 nd order nature of the phase transition. High resolution XRD was performed by Lu Cai at 100 K, 295 K, 345 K and 400 K an d confirmed a phase transition. The high temperature phase was refined to
134 Cmcm while significant controversy remained over the low temperature phase between C 222 1 and Cm2m due to their nearly identical XRD refinement. The dielectric behavior of Gd 3 TaO 7 wa s characterized as a function of temperature, at the phase transition point the real part of the permittivity exhibit a sharp decrease as a function of temperature. Unlike Gd 3 nbO 7 Gd 3 TaO 7 does not display peaks in the imaginary component of the permittivi ty, the phase transition of Gd 3 TaO 7 is known to go from the Cmcm to C 222 1 The difference in the dielectric loss response of Gd 3 TaO 7 and Gd 3 NbO 7 point to a different type of phase transition and the proposed polar group of Cm2m would account for the differ ence in the dielectric behavior.
135 CHAPTER 10 SUMMARY AND FUTURE WORK 10 .1 Summary The investigation for materials with high permittivity and low loss is necessary for the advancement of electronic components. The work reported in this thesis investigates t he structure dielectric properties of Bi 2 Ti 2 O 7 and defect fluorites, as well as uncovering the true cause for the dielectric relaxation phenomena in bismuth pyrochlores. Microwave sintering was used to sinter Bi 2 Ti 2 O 7 and dielectric spectroscopy, Raman and IR spectroscopy, and Neutron and HR XRD as a function of temperature were performed and characterized for the first time in reported literature. The structural characterization of (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 (x = 0.25, 0.5, 0.75) was presented here. It was found that both systems formed a phase pure pyrochlore phase and the presence of the (442) diffraction peak was not detected. Therefore, both of the Sm systems only have the presence of substitution and do not have atomic displacements found i n most Bi pyrochlores. A more in depth structural study of Bi 2 Ti 2 O 7 was performed using neutron diffraction, synchrotron x ray diffraction (SXRD), and DFT. Both the neutron and SXRD revealed displacements of the Bi cation to the 96 g site and the displaceme nt of the showed a better fit when vacancies were considered on the Bi and O(1) site, the energy of formation of non stoichiometric Bi 2 Ti 2 O 7 was found to be 3.13 eV at room temperature. A dielectric analysis of Bi 2 Ti 2 O 7 ceramic, a bismuth pyrochlore without substitutional disorder, revealed considerable differences with respect to the common dielectric behavior exhibited by this family of compounds. The dielectric relaxation
136 observed in BZN is absent in Bi 2 Ti 2 O 7 ; however, a rela xation of a different nature was found at low frequencies (<10 kHz) and at relatively high temperature (125 K) in Bi 2 Ti 2 O 7 The calculated activation energy and characteristic frequency of this behavior using the Arrhenius model were 0.162 eV and ~1 MHz, respectively. The low attempt jump frequency is consistent with space charge polarization and not the result of dipolar or ionic disorder. The relaxation behavior at low frequency was confirmed with a study nd impedance as a function of frequency. The atypical dielectric response of Bi 2 Ti 2 O 7 suggests that substitutional cations (rather than ionic displacements, or lone pair electrons), play a major role in the origin of the dielectric relaxation in pyrochlore s. A dielectric analysis of the (Sm x Yb 1 x ) 2 Ti 2 O 7 and Sm 2 (Sn x Ti 1 x ) 2 O 7 ( x = 0.25, 0.5, 0.75) systems, pyrochlores without atomic displacements, revealed no evidence of dielectric relaxation to that observed in BZN. These responses suggest that substitutiona l cations The Raman spectra of the pyrochlore Bi 2 Ti 2 O 7 was measured on both calcined powder and sintered ceramic Raman modes were assigned by comparison to other bismuth and titanate pyrochlores found in literature, Bi 2 Ti 2 O 7 displays evidence of displaciv e disorder in both the A and B site. A low frequency F 1u mode (normally IR active) is assigned in the Raman spectra, due to the relaxation of the selection rules resulting from the displacement of the Bi atom from its ideal crystallographic position. Add itionally, evidence of displacement in the Ti atomic position is provided by the atypical spectroscopic behavior of the Ti O modes at the higher range of the Raman spectra. The IR spectra were fit to an oscillator model from which the real and imaginary p arts of the dielectric function were obtained. The low frequency O A O and
137 A n displacement. The dielectric properties of type II Bi 3 O 7 single crystal were investigated as a function of frequency and temperature. The dielectric response of type II Bi 3 NbO 7 follows the same behavior as the Ln 3 NbO 7 defect fluorite series, where the real part of the permittivity decreases with decreasing temperature. Due to the fact that bismuth is highly polarizable is displays a permittivity of 85 at room temperature (1 MHz). The dielectric behavior as a function of frequency was also investigated and the onset of electrical conduction was identified at around 473 K. The TCC of Ln 3 NbO 7 decreases with increasing Ln 3+ ionic radius and type II Bi 3 NbO 7 was found to be 1.53x10 3 ppm/C and followed the same general trend. T he work presented in this dissertation adds a final link to the question of what conditions are required in pyrochlores to exhibit dielectric relaxation An in depth investigation into the structure and dielectric properties of Bi 2 Ti 2 O 7 showed that a pyrochlore displaying atomic displacements without substitution does not display relaxation. This result points suggests that substitutional cations play a major role in the origin of dielectric relaxation in pyrochlores. 10 .2 Future Work A study into the local structure of Bi 2 Ti 2 O 7 through TEM would give further insight into the proposed correlated displacements of the Bi cation in Bi 2 Ti 2 O 7 The synthesis of dielectric thin films of Bi 2 Ti 2 O 7 would allow for a comparison of the properties with bulk Bi 2 Ti 2 O 7 Raman measurements as a function of temperature o f Bi 2 Ti 2 O 7 would also compliment the already measure IR data. An investigation into the dielectric properties
138 at microwave frequencies for all the pyrochlores synthesized in this work would shed some light on the microwave dielectric properties of the synt hesized pyrochlores.
139 APPENDIX A EQUIVALENT CIRCUIT A NALYSIS OF Bi 2 Ti 2 O 7 A.1. Introduction Compounds with the nominal composition A 2 B 2 O 7 containing the B 2 O 6 octahedral and the A 2 structures are known as pyrochlores. Bismuth based pyrochl ores have been extensively studied due to their attractive composition dependent dielectric properties. 12 13 20 24 71 162 A combination of high permittivity values (usually above 100), low dielectric loss, and low s intering temperatures (1000C 150) makes them good materials for dielectric components for embedded capacitors and multilayer ceramic capacitors (MLCC). The recent findings presented in Chapter 5 showed that Bi 2 Ti 2 O 7 did not display typical bismuth pyroc hlore relaxation, as seen in Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 (BZN), a relaxation of a different nature was found at low frequencies (<10kHz) and at relatively high temperatures (125 K) in Bi 2 Ti 2 O 7 The calculated low attempt jump frequency of ~1 MHz is consistent with space charge polarization. Equivalent circuit analysis provides a good basis for the understanding of the electrical behavior as physical processes can be assigned to capacitor (C), resistor (R), and constant phase elements (CPE) components. Recentl y, the electrical properties of both bismuth zinc niobate titanate (BZNT) 163 and BZN 164 have been characterized using equivalent circuit analysis by Osman and coworkers in an effort to understand the origin of the relaxor like behavior displayed by bo th BZNT and BZN. The main objective is to characterize the space charge dielectric relaxation behavior of Bi 2 Ti 2 O 7 using equivalent circuits that model the impedance data from room
140 temperature to 30 K, in order to provide a model of the electrical response of Bi 2 Ti 2 O 7 compared to other pyrochlores that display typical Bi pyrochlore relaxation behavior A.2. Equivalent C ircuit A nalysis Equivalent circuit analysis is commonly used to model impedance spectroscopy data in terms of ideal circuit elements (R,L, a nd C). The circuit elements are commonly used to provide a physical interpretation of the electrical response of the material 165 Recently, Osman and West have applied equivalent circuit analysis to relaxor ceramics in order to furt her characterize and understand the nature of dielectric relaxation in ceramics 166 167 There has not, however, been an equivalent circuit that models dielectric relaxation due to space charge polarization. In order to find an appropriate equivalent circuit response the experimental xtracted from the impedance measurements is shown as a function of frequency for a selection of temperatures over the range of 30K to 300K in Figure A 1 At low temperatures, 30K lower values with increasing frequency. Temperatures between 190K 300K display an higher frequencies as the temperature increases. This increase in capacitance is most likely due to the relaxation ev ent occurring at lower frequencies at these temperatures, shown in Chapter 5.
141 A B C Figure A 1 Cap A) 300K 190K, B) 190K 30K and C ) 300K 30K. shown from the temperature range of 30 K 300 K against frequency on logarithmic scales in Figure A 2 The data below 170 K show a frequency dependent admittance
142 tempera to the low frequency, moderate temperature relaxation occurring in Bi 2 Ti 2 O 7 Figure A 2 300K From the data shown in Figure A 2 there are two different responses as the temperature decreases. From 300K 190K there is low frequency relaxation which can be modeled by the equivalent circuit shown in Figure A 3A this circuit is similar to what Osman and West proposed for (Bi 1.5 Zn 0.5 )(Nb 0.5 Ti 1.5 )O 7 relaxation process 166 but in Bi 2 Ti 2 O 7 an extra R and C element are added in parallel to model the loss of capacitance at higher frequencies.
143 A B Figure A 3 Equivalent circuit showing different R, C, and CPE combinations Figure A 4 shows the capacitance and admittance data and the fit of the equivalent circuit at 210K. As the temperature drops below 190K the relaxation event occurring at low frequ encies is n o longer evident ( Figure A 3 A ), therefore R 1 was eliminated from the circuit and the CPE was maintained due to the linear power law dependence with a slope greater than 1 is still exhibited at temperatures below 180K. Figure A 5 shows the equiva lent circuit fit at 110K using the equivalent circuit from Figure A 3 B
144 A B Figure A 4 Fit of the 210K to circuit in Figure A 3
145 A) B Figure A 5 Fit of the 210K to circuit in Figure A 3 B for The equi valent circuits give a potential insight into the electrical response of spectroscopic plots the equivalent circuit cannot be fit using only R and C components
146 alone, and by introducing a constant phase element (CPE) into both equivalent circuits a good fit is observed. The circuit, Figure A 3A is a proposed circuit model for dielectric relaxation due to space charge polarization.
147 APPENDIX B Bi2Ti2O7 TEMPERATURE EFFECTS ON STRUCTURE AND DIE LECTRIC PROPERTIES The data presented in this dissertation along with low temperature heat capacity are all presented as a function of temperature. Figure B 1 attempts to show the low temperature anomalies in each dataset (permittivity neutron, heat capacity) and show any correlation between the structure/phase changes and dielectric properties. Both the neutron and specific heat capacity (Cp) performed at low temperatures revealed an anomaly. The lattice saturation at low temperatures discussed in Chapter 4 occurs at 210 K and the specific heat shows a deviation at 127 K. When overlaying these anomalies on the dielectric properties it is interesting to note that at 127 K is where the dielectric relaxation stops appearing in Bi 2 Ti 2 O 7 I n fact the analysis as a function of frequency shows that under 130 K the relaxation behavior is no longer present. The lattice stiffening temperature of 210 K does not correlate with the dielectric or Cp measurements, however, at 127 K the lattice stiffen ing seems to be clearer indicating a possible correlation between the Cp, neutron, and dielectric permittivity.
148 Figure B 1. A comparison of the temperature anomalies found in the specific heat, neutron diffraction and dielectric permittivity.
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163 BIOGRAPHICAL SKETCH Christopher Turner was born i n Santiago, Chile in 1987. He has since lived in Redondo Beach (California, USA), Sao Paulo (Brazil), Bangkok (Thailand) and finally Weston, Florida in 2004 where he graduated from Cypress Bay High School in 2006. Christopher began attending the Universit y of Florida the following June and graduated with a B.S. in Materials Science and Engineering, specializing in Biomaterials, in May of spending nearly 8 years and 3 nati onal championships at UF in Gainesville, he received his Ph.D. in the Spring of 2014.